The Experts below are selected from a list of 21819 Experts worldwide ranked by ideXlab platform

Patricia J Y Wong - One of the best experts on this subject based on the ideXlab platform.

Ravi P Agarwal - One of the best experts on this subject based on the ideXlab platform.

Donal O'regan - One of the best experts on this subject based on the ideXlab platform.

  • Constant Sign solutions for parameter-dependent superlinear second-order difference equations
    Journal of Difference Equations and Applications, 2015
    Co-Authors: Pasquale Candito, Giuseppina D'aguì, Donal O'regan
    Abstract:

    This paper studies the existence of Constant Sign solutions for a second-order parameter-dependent super linear difference equation. The approach is based on variational methods on finite dimensional Banach spaces.

  • A variational approach to nonlinear logistic equations
    Communications in Contemporary Mathematics, 2015
    Co-Authors: Leszek Gasiński, Donal O'regan, Nikolaos S. Papageorgiou
    Abstract:

    We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of Constant Sign and in fact we establish the existence of extremal Constant Sign solutions. Using these extremal solutions, we produce a nodal (Sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

  • System of Fredholm Integral Equations: Existence of a Constant-Sign Solution
    Constant-Sign Solutions of Systems of Integral Equations, 2013
    Co-Authors: Ravi P Agarwal, Donal O'regan, Patricia J Y Wong
    Abstract:

    In this chapter we shall consider two systems of integral equations, one is on a finite interval $$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ (5.1.1) and the other is on the half-line [0, ∞) $$\displaystyle{ u_{i}(t) =\int _{ 0}^{\infty }g_{ i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,\infty ),\ 1 \leq i \leq n. }$$ (5.1.2) In both (5.1.1) and (5.1.2), we shall include both cases when the function f is “nonnegative” as well as when f may take “negative” values.

  • System of Integral Equations: Constant-Sign Periodic and Almost Periodic Solutions
    Constant-Sign Solutions of Systems of Integral Equations, 2013
    Co-Authors: Ravi P Agarwal, Donal O'regan, Patricia J Y Wong
    Abstract:

    In this chapter we shall consider two systems of Hammerstein integral equations, one is on a real interval I $$\displaystyle{ u_{i}(t) =\int _{I}g_{i}(t,s)f(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in I,\ 1 \leq i \leq n }$$ (15.1.1) and the other is on \(\mathbb{R}\) $$\displaystyle{ u_{i}(t) =\int _{\mathbb{R}}g_{i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in \mathbb{R},\ 1 \leq i \leq n. }$$ (15.1.2)

  • System of Fredholm Integral Equations: Triple Constant-Sign Solutions
    Constant-Sign Solutions of Systems of Integral Equations, 2013
    Co-Authors: Ravi P Agarwal, Donal O'regan, Patricia J Y Wong
    Abstract:

    In this chapter we shall consider two systems of Fredholm integral equations, one is on a finite interval $$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)P_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ (4.1.1) and the other is on the half-line [0,∞) $$\displaystyle{ u_{i}(t) =\int _{ 0}^{\infty }g_{ i}(t,s)P_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,\infty ),\ 1 \leq i \leq n. }$$ (4.1.2)

Nikolaos S. Papageorgiou - One of the best experts on this subject based on the ideXlab platform.

  • Constant Sign and nodal solutions for superlinear double phase problems
    Advances in Calculus of Variations, 2019
    Co-Authors: Leszek Gasiński, Nikolaos S. Papageorgiou
    Abstract:

    Abstract We consider a double phase problems with unbalanced growth and a superlinear reaction, which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools and the Nehari method, we show that the Dirichlet problem has at least three nontrivial solutions, a positive solution, a negative solution and a nodal solution. The nodal solution has exactly two nodal domains.

  • Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition
    Journal of Optimization Theory and Applications, 2017
    Co-Authors: Nikolaos S. Papageorgiou, Vicenţiu D Rădulescu, Dušan D. Repovš
    Abstract:

    We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of Constant Sign and the third nodal. We also show the existence of extremal Constant Sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).

  • A variational approach to nonlinear logistic equations
    Communications in Contemporary Mathematics, 2015
    Co-Authors: Leszek Gasiński, Donal O'regan, Nikolaos S. Papageorgiou
    Abstract:

    We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of Constant Sign and in fact we establish the existence of extremal Constant Sign solutions. Using these extremal solutions, we produce a nodal (Sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

  • Constant Sign and nodal solutions for a class of nonlinear Dirichlet problems
    Journal of Mathematical Analysis and Applications, 2015
    Co-Authors: Nikolaos S. Papageorgiou, Sandrina Rafaela Andrade Santos, Vasile Staicu
    Abstract:

    Abstract We consider a nonlinear Dirichlet problem with a Caratheodory reaction which has arbitrary growth from below. We show that the problem has at least three nontrivial smooth solutions, two of Constant Sign and the third nodal. In the semilinear case (i.e., p = 2 ), with the reaction f ( z , . ) being C 1 and with subcritical growth, we show that there is a second nodal solution, for a total of four nontrivial smooth solutions. Finally, when the reaction has concave terms and is subcritical and for the nonlinear problem (i.e., 1 p ∞ ) we show that again we can have the existence of three nontrivial smooth solutions, two of Constant Sign and a third nodal.

  • Constant Sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities
    Methods and Applications of Analysis, 2015
    Co-Authors: Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu
    Abstract:

    We study a parametric nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which is ”concave” (i.e., (p − 1)− sublinear) near zero and ”convex” (i.e., (p − 1)− superlinear) near ±1. Using variational methods combined with truncation and comparison techniques, we show that for all small values of the parameter > 0, the problem has at least five nontrivial smooth solutions (four of Constant Sign and the fifth nodal). In the Hilbert space case (p = 2), using Morse theory, we produce a sixth nontrivial smooth solution but we do not determine its Sign

Lorena Saavedra - One of the best experts on this subject based on the ideXlab platform.

  • Constant Sign solution for simply supported beam equation with non-homogeneous boundary conditions
    arXiv: Classical Analysis and ODEs, 2017
    Co-Authors: Alberto Cabada, Lorena Saavedra
    Abstract:

    The aim of this paper is to study the following fourth-order operator: T[p,c]\,u(t)\equiv u^{(4)}(t)-p\,u"(t)+c(t)\,u(t)\,,\quad t\in I\equiv [a,b]\,, coupled with the non-homogeneous simply supported beam boundary conditions: u(a)=u(b)=0\,,\quad u"(a)=d_1\leq0\,,\ u"(b)=d_2\leq 0\,. First, we prove a result which makes an equivalence between the strongly inverse positive (negative) character of this operator with the previously introduced boundary conditions and with the homogeneous boundary conditions, given by: T[p,c]\,u(t)=h(t)(\geq0)\,, u(a)=u(b)=u"(a)=u"(b)=0\,, Once that we have done that, we prove several results where the strongly inverse positive (negative) character of $T[p,c]$ it is ensured. Finally, there are shown a couple of result which say that under the hypothesis that $h>0$, we can affirm that the problem for the homogeneous boundary conditions has a unique Constant Sign solution.

  • Constant Sign Green’s function for simply supported beam equation.∗
    arXiv: Classical Analysis and ODEs, 2016
    Co-Authors: Alberto Cabada, Lorena Saavedra
    Abstract:

    The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u"(a)=u"(b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C^4(I)\quad\mid\quad u(a)=u(b)=u"(a)=u"(b)=0 \right\rbrace \,. \end{equation} Here $p_1\in C^3(I)$ and $p_2\in C^2(I)$. By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is disconjugate on $I$, we characterize the parameter's set where the Green's function related to operator $T[M]$ in $X$ is of Constant Sign on $I \times I$. Such characterization is equivalent to the strongly inverse positive (negative) character of operator $T[M]$ on $X$ and comes from the first eigenvalues of operator $T[0]$ on suitable spaces.

  • Constant Sign green s function for simply supported beam equation
    arXiv: Classical Analysis and ODEs, 2016
    Co-Authors: Alberto Cabada, Lorena Saavedra
    Abstract:

    The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u"(a)=u"(b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C^4(I)\quad\mid\quad u(a)=u(b)=u"(a)=u"(b)=0 \right\rbrace \,. \end{equation} Here $p_1\in C^3(I)$ and $p_2\in C^2(I)$. By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is disconjugate on $I$, we characterize the parameter's set where the Green's function related to operator $T[M]$ in $X$ is of Constant Sign on $I \times I$. Such characterization is equivalent to the strongly inverse positive (negative) character of operator $T[M]$ on $X$ and comes from the first eigenvalues of operator $T[0]$ on suitable spaces.

  • The eigenvalue characterization for the Constant Sign Green’s functions of ( k , n − k ) problems
    Boundary Value Problems, 2016
    Co-Authors: Alberto Cabada, Lorena Saavedra
    Abstract:

    This paper is devoted to the study of the Sign of the Green’s function related to a general linear nth-order operator, depending on a real parameter, $T_{n}[M]$ , coupled with the $(k,n-k)$ boundary value conditions. If the operator $T_{n}[\bar{M}]$ is disconjugate for a given M, we describe the interval of values on the real parameter M for which the Green’s function has Constant Sign. One of the extremes of the interval is given by the first eigenvalue of the operator $T_{n}[\bar{M}]$ satisfying $(k,n-k)$ conditions. The other extreme is related to the minimum (maximum) of the first eigenvalues of $(k-1,n-k+1)$ and $(k+1,n-k-1)$ problems. Moreover, if $n-k$ is even (odd) the Green’s function cannot be nonpositive (nonnegative). To illustrate the applicability of the obtained results, we calculate the parameter intervals of Constant Sign Green’s functions for particular operators. Our method avoids the necessity of calculating the expression of the Green’s function. We finalize the paper by presenting a particular equation in which it is shown that the disconjugation hypothesis on operator $T_{n}[\bar{M}]$ for a given M cannot be eliminated.

  • the eigenvalue characterization for the Constant Sign green s functions of k n k problems
    Boundary Value Problems, 2016
    Co-Authors: Alberto Cabada, Lorena Saavedra
    Abstract:

    This paper is devoted to the study of the Sign of the Green’s function related to a general linear nth-order operator, depending on a real parameter, $T_{n}[M]$ , coupled with the $(k,n-k)$ boundary value conditions. If the operator $T_{n}[\bar{M}]$ is disconjugate for a given M, we describe the interval of values on the real parameter M for which the Green’s function has Constant Sign. One of the extremes of the interval is given by the first eigenvalue of the operator $T_{n}[\bar{M}]$ satisfying $(k,n-k)$ conditions. The other extreme is related to the minimum (maximum) of the first eigenvalues of $(k-1,n-k+1)$ and $(k+1,n-k-1)$ problems. Moreover, if $n-k$ is even (odd) the Green’s function cannot be nonpositive (nonnegative). To illustrate the applicability of the obtained results, we calculate the parameter intervals of Constant Sign Green’s functions for particular operators. Our method avoids the necessity of calculating the expression of the Green’s function. We finalize the paper by presenting a particular equation in which it is shown that the disconjugation hypothesis on operator $T_{n}[\bar{M}]$ for a given M cannot be eliminated.