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Vy Khoi Le - One of the best experts on this subject based on the ideXlab platform.
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on variational inequalities with maximal monotone operators and multivalued perturbing terms in sobolev spaces with variable exponents
Journal of Mathematical Analysis and Applications, 2012Co-Authors: Vy Khoi LeAbstract:Abstract We are concerned in this paper with variational inequalities of the form: { 〈 A ( u ) , v − u 〉 + 〈 F ( u ) , v − u 〉 ⩾ 〈 L , v − u 〉 , ∀ v ∈ K , u ∈ K , where A is a maximal monotone operator, F is an integral multivalued lower order term, and K is a closed, convex set in a Sobolev space of variable exponent. We study both coercive and noncoercive inequalities. In the noncoercive case, a sub-Supersolution approach is followed to obtain the existence and some other qualitative properties of solutions between sub- and Supersolutions.
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on a sub Supersolution method for variational inequalities with leray lions operators in variable exponent spaces
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Vy Khoi LeAbstract:Abstract In this paper, we consider a sub–Supersolution method for variational inequalities with Leray–Lions operators in Sobolev spaces with variable exponents. Existence and qualitative properties of solutions between sub and Supersolutions are established.
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On a sub―Supersolution method for variational inequalities with Leray―Lions operators in variable exponent spaces
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Vy Khoi LeAbstract:Abstract In this paper, we consider a sub–Supersolution method for variational inequalities with Leray–Lions operators in Sobolev spaces with variable exponents. Existence and qualitative properties of solutions between sub and Supersolutions are established.
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on a sub Supersolution method for the prescribed mean curvature problem
Czechoslovak Mathematical Journal, 2008Co-Authors: Vy Khoi LeAbstract:The paper is about a sub-Supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub-and Supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub-and Supersolutions are established.
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Some general concepts of sub- and Supersolutions for nonlinear elliptic problems
Topological Methods in Nonlinear Analysis, 2006Co-Authors: Vy Khoi Le, Klaus SchmittAbstract:We propose general and unified concepts of sub- Supersolutions for boundary value problems that encompass several types of boundary conditions for nonlinear elliptic equations and variational inequalities. Various, by now classical, sub- and Supersolution existence and comparison results are covered by the general theory presented here.
Dragospatru Covei - One of the best experts on this subject based on the ideXlab platform.
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Existence of solution for a class of nonlocal elliptic problem via sub–Supersolution method
Nonlinear Analysis-real World Applications, 2015Co-Authors: Claudianor O Alves, Dragospatru CoveiAbstract:Abstract We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and Supersolution with the pseudomonotone operators theory.
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existence of solution for a class of nonlocal elliptic problem via sub Supersolution method
Nonlinear Analysis-real World Applications, 2015Co-Authors: Claudianor O Alves, Dragospatru CoveiAbstract:Abstract We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and Supersolution with the pseudomonotone operators theory.
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existence of solution for a class of nonlocal elliptic problem combining variational methods with the sub Supersolution method
2013Co-Authors: Claudianor O Alves, Dragospatru CoveiAbstract:We show the existence of solution for some classes of nonlocal problems. Our proof combines variational methods in the presence of a sub and Supersolution.
Siegfried Carl - One of the best experts on this subject based on the ideXlab platform.
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Quasilinear parabolic variational inequalities with multi-valued lower-order terms
Zeitschrift für angewandte Mathematik und Physik, 2014Co-Authors: Siegfried Carl, Vy K. LeAbstract:In this paper, we provide an analytical frame work for the following multi-valued parabolic variational inequality in a cylindrical domain $${Q = \Omega \times (0, \tau)}$$ Q = Ω × ( 0 , τ ) : Find $${{u \in K}}$$ u ∈ K and an $${{\eta \in L^{p'}(Q)}}$$ η ∈ L p ′ ( Q ) such that $$\eta \in f(\cdot,\cdot,u), \quad \langle u_t + Au, v - u\rangle + \int_Q \eta (v - u)\,{\rm d}x{\rm d}t \ge 0, \quad \forall \, v \in K,$$ η ∈ f ( · , · , u ) , 〈 u t + Au , v − u 〉 + ∫ Q η ( v − u ) d x d t ≥ 0 , ∀ v ∈ K , where $${{K \subset X_0 = L^p(0,\tau;W_0^{1,p}(\Omega))}}$$ K ⊂ X 0 = L p ( 0 , τ ; W 0 1 , p ( Ω ) ) is some closed and convex subset, A is a time-dependent quasilinear elliptic operator, and the multi-valued function $${{s \mapsto f(\cdot,\cdot,s)}}$$ s ↦ f ( · , · , s ) is assumed to be upper semicontinuous only, so that Clarke’s generalized gradient is included as a special case. Thus, parabolic variational–hemivariational inequalities are special cases of the problem considered here. The extension of parabolic variational–hemivariational inequalities to the general class of multi-valued problems considered in this paper is not only of disciplinary interest, but is motivated by the need in applications. The main goals are as follows. First, we provide an existence theory for the above-stated problem under coercivity assumptions. Second, in the noncoercive case, we establish an appropriate sub-Supersolution method that allows us to get existence, comparison, and enclosure results. Third, the order structure of the solution set enclosed by sub-Supersolutions is revealed. In particular, it is shown that the solution set within the sector of sub-Supersolutions is a directed set. As an application, a multi-valued parabolic obstacle problem is treated.
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the sub and Supersolution method for variational hemivariational inequalities
Nonlinear Analysis-theory Methods & Applications, 2008Co-Authors: Siegfried CarlAbstract:Abstract The well-known method of sub- and Supersolutions is a powerful tool for proving existence and comparison results for initial and/or boundary value problems of nonlinear ordinary differential equations as well as for nonlinear partial differential equations of elliptic and parabolic type. The main goal of this paper is to extend the idea of the sub- and Supersolution method in a natural and systematic way to quasilinear elliptic variational–hemivariational inequalities. Owing to the intrinsic asymmetry of the latter (where the problems are stated as inequalities rather than as equalities) an appropriate generalization of the notion of sub- and Supersolutions to variational–hemivariational inequalities is by no means straightforward. The obtained results of this paper complement the development of the sub- and Supersolution method for nonsmooth variational problems presented in a recent monograph by S. Carl, Vy K. Le and D. Motreanu.
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The sub- and Supersolution method for variational–hemivariational inequalities
Nonlinear Analysis-theory Methods & Applications, 2008Co-Authors: Siegfried CarlAbstract:Abstract The well-known method of sub- and Supersolutions is a powerful tool for proving existence and comparison results for initial and/or boundary value problems of nonlinear ordinary differential equations as well as for nonlinear partial differential equations of elliptic and parabolic type. The main goal of this paper is to extend the idea of the sub- and Supersolution method in a natural and systematic way to quasilinear elliptic variational–hemivariational inequalities. Owing to the intrinsic asymmetry of the latter (where the problems are stated as inequalities rather than as equalities) an appropriate generalization of the notion of sub- and Supersolutions to variational–hemivariational inequalities is by no means straightforward. The obtained results of this paper complement the development of the sub- and Supersolution method for nonsmooth variational problems presented in a recent monograph by S. Carl, Vy K. Le and D. Motreanu.
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Comparison results for a class of quasilinear evolutionary hemivariational inequalities
2007Co-Authors: Siegfried CarlAbstract:We consider a class of quasilinear evolutionary hemivariational inequalities under nonmonotone multivalued flux boundary conditions. Our main goal is to provide existence and comparison results in terms of appropriately defined sub- and Supersolutions on the basis of which one can prove compactness and extremality results of the solution set within the sector of sub- and Supersolutions.
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Existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems
Nonlinear Analysis-theory Methods & Applications, 2006Co-Authors: Siegfried CarlAbstract:Abstract We consider noncoercive quasilinear elliptic inclusions under multivalued flux boundary conditions involving multifunctions of Clarke’s generalized gradient. Our main goal is to provide existence and comparison results which are based on an appropriate generalization of the notions of subsolutions and Supersolutions. Furthermore, compactness and extremality results of the solution set enclosed by an ordered pair of sub–Supersolutions will be proved.
Leandro S Tavares - One of the best experts on this subject based on the ideXlab platform.
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sub Supersolution method for a singular problem involving the φ laplacian and orlicz sobolev spaces
Complex Variables and Elliptic Equations, 2020Co-Authors: Giovany M Figueiredo, Gelson Dos C G Santos, Leandro S TavaresAbstract:ABSTRACTIn this manuscript we study the existence and multiplicity of solutions for a singular equation involving Orlicz–Sobolev spaces. The approach is based on sub-Supersolutions and variational ...
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a sub Supersolution approach for some classes of nonlocal problems involving orlicz spaces
Journal of Differential Equations, 2019Co-Authors: Giovany M Figueiredo, Gelson Dos C G Santos, Abdelkrim Moussaoui, Leandro S TavaresAbstract:Abstract In the present paper we study the existence of solutions for some nonlocal problems involving Orlicz-Sobolev spaces. The approach is based on sub-Supersolutions.
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Existence Results for Some Anisotropic Singular Problems via Sub-Supersolutions
Milan Journal of Mathematics, 2019Co-Authors: Gelson C. G. Dos Santos, Giovany M Figueiredo, Leandro S TavaresAbstract:In this manuscript it is proved existence results for some singular problems involving an anisotropic operator. In the approach we combine sub-Supersolutions, truncation arguments and the Schaefer’s Fixed Point Theorem [23]. In this work it is not used approximation arguments as in [33, 37]
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a sub Supersolution method for a class of nonlocal problems involving the p x p x laplacian operator and applications
Acta Applicandae Mathematicae, 2018Co-Authors: Gelson Dos C G Santos, Giovany M Figueiredo, Leandro S TavaresAbstract:In the present paper, we study the existence of solutions for some nonlocal problems involving the $p(x)$ -Laplacian operator. The approach is based on a new sub-Supersolution method.
Giovany M Figueiredo - One of the best experts on this subject based on the ideXlab platform.
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sub Supersolution method for a singular problem involving the φ laplacian and orlicz sobolev spaces
Complex Variables and Elliptic Equations, 2020Co-Authors: Giovany M Figueiredo, Gelson Dos C G Santos, Leandro S TavaresAbstract:ABSTRACTIn this manuscript we study the existence and multiplicity of solutions for a singular equation involving Orlicz–Sobolev spaces. The approach is based on sub-Supersolutions and variational ...
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sub Supersolution method for a quasilinear elliptic problem involving the 1 laplacian operator and a gradient term
Journal of Functional Analysis, 2020Co-Authors: Giovany M Figueiredo, Marcos T O PimentaAbstract:Abstract In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in B V ( Ω ) , having no jump part. Despite the lack of regularity of the solutions, we develop a sub-Supersolution approach, together with a thorough analysis of the distributional derivative of the functions in B V ( Ω ) .
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a sub Supersolution approach for some classes of nonlocal problems involving orlicz spaces
Journal of Differential Equations, 2019Co-Authors: Giovany M Figueiredo, Gelson Dos C G Santos, Abdelkrim Moussaoui, Leandro S TavaresAbstract:Abstract In the present paper we study the existence of solutions for some nonlocal problems involving Orlicz-Sobolev spaces. The approach is based on sub-Supersolutions.
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Existence Results for Some Anisotropic Singular Problems via Sub-Supersolutions
Milan Journal of Mathematics, 2019Co-Authors: Gelson C. G. Dos Santos, Giovany M Figueiredo, Leandro S TavaresAbstract:In this manuscript it is proved existence results for some singular problems involving an anisotropic operator. In the approach we combine sub-Supersolutions, truncation arguments and the Schaefer’s Fixed Point Theorem [23]. In this work it is not used approximation arguments as in [33, 37]
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a sub Supersolution method for a class of nonlocal problems involving the p x p x laplacian operator and applications
Acta Applicandae Mathematicae, 2018Co-Authors: Gelson Dos C G Santos, Giovany M Figueiredo, Leandro S TavaresAbstract:In the present paper, we study the existence of solutions for some nonlocal problems involving the $p(x)$ -Laplacian operator. The approach is based on a new sub-Supersolution method.
