The Experts below are selected from a list of 15135 Experts worldwide ranked by ideXlab platform
Shaowei Chen - One of the best experts on this subject based on the ideXlab platform.
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existence of a Nontrivial Solution for a strongly indefinite periodic choquard system
Calculus of Variations and Partial Differential Equations, 2015Co-Authors: Shaowei Chen, Liqin XiaoAbstract:We consider the Choquard system $$\begin{aligned} \left\{ \begin{array} [c]{ll} -\Delta u+V( x) u+|u|^{p-2}u=\lambda \phi u , &{}\quad \text{ in } \mathbb {R}^{3},\\ -\Delta \phi = u^{2}, &{}\quad \text{ in } \mathbb {R}^{3}. \end{array} \right. \end{aligned}$$ where \(\lambda >0\) is a parameter, \(3 0,\) this system has a Nontrivial Solution.
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existence of Nontrivial Solution for a 4 sublinear schrodinger poisson system
Applied Mathematics Letters, 2014Co-Authors: Shaowei Chen, Dawei ZhangAbstract:Abstract We consider a Schrodinger–Poisson system in R 3 with potential indefinite in sign and a general 4-sublinear nonlinearity. Its variational functional does not satisfy the Palais–Smale condition in general. We use a finite-dimensional approximation method to obtain a sequence of approximate Solutions. Then we prove that these approximate Solutions converge weakly to a Nontrivial Solution of this system.
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existence of a Nontrivial Solution for a strongly indefinite periodic schrodinger poisson system
arXiv: Analysis of PDEs, 2014Co-Authors: Shaowei Chen, Liqian XiaoAbstract:We consider the Schr\"odinger-Poisson system \begin{eqnarray}\left\{\begin{array} [c]{ll} -\Delta u+V(x) u+|u|^{p-2}u=\lambda \phi u, & \mbox{in}\mathbb{R}^{3},\\ -\Delta\phi= u^{2}, & \mbox{in}\mathbb{R}^{3}. \end{array} \right.\nonumber \end{eqnarray} where $\lambda>0$ is a parameter, $3< p<6$, $V\in C(\mathbb{R}^{3}) $ is $1$-periodic in $x_j$ for $j = 1,2,3$ and 0 is in a spectral gap of the operator $-\Delta+V$. This system is strongly indefinite, i.e., the operator $-\Delta+V$ has infinite-dimensional negative and positive spaces and it has a competitive interplay of the nonlinearities $|u|^{p-2}u$ and $\lambda \phi u$. Moreover, the functional corresponding to this system does not satisfy the Palai-Smale condition. Using a new infinite-dimensional linking theorem, we prove that, for sufficiently small $\lambda>0,$ this system has a Nontrivial Solution.
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Nontrivial Solution for a semilinear elliptic equation in unbounded domain with critical sobolev exponent
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Shaowei ChenAbstract:where Ω is an unbounded domains with smooth boundary in R , 2∗ = 2N/ (N − 2), a(x) ∈C1(Ω) satisfies the following conditions: (A1) a ∈ LN/2(Ω). (A2) Ω− = {x ∈Ω | a(x) 0 such that B(θ,4δ)⊂⊂Ω−. When Ω is a bounded domain with smooth boundary in R (N 5), similar problem has been studied by many mathematicians; for example, in [3], Brezis and Nirenberg studied problem (P). In [4], Capozzi et al. prove that when Ω
Aixia Qian - One of the best experts on this subject based on the ideXlab platform.
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On the existence of Nontrivial Solutions for a fourth-order semilinear elliptic problem
Abstract and Applied Analysis, 2005Co-Authors: Aixia QianAbstract:By means of Minimax theory, we study the existence of one Nontrivial Solution and multiple Nontrivial Solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.
Xiaojing Feng - One of the best experts on this subject based on the ideXlab platform.
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Nontrivial Solution for schrodinger poisson equations involving the fractional laplacian with critical exponent
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2021Co-Authors: Xiaojing FengAbstract:This paper deals with a class of nonlocal Schrodinger equations with critical exponent $$\begin{aligned} \left\{ \begin{array}{llll} (-\Delta )^{s} u+V(x)u-K(x)\phi |u|^{2^*_s-3}u=f(x,u),&{}\quad \mathrm{in}\ \mathbb {R}^3,\\ (-\Delta )^s \phi =K(x)|u|^{2^*_s-1},&{}\quad \mathrm{in}\ \mathbb {R}^3. \end{array}\right. \end{aligned}$$ By employing the mountain pass theorem, concentration-compactness principle and approximation method, the existence of Nontrivial Solution is obtained under appropriate assumptions on V, K and f.
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Nontrivial Solution for schrodinger poisson equations involving a fractional nonlocal operator via perturbation methods
Zeitschrift für Angewandte Mathematik und Physik, 2016Co-Authors: Xiaojing FengAbstract:This paper focuses on the following Schrodinger–Poisson equations involving a fractional nonlocal operator \({\left\{\begin{array}{ll}-\Delta u+u+\phi u=f(x,u),&{\rm in}\ \mathbb{R}^3,\\(-\Delta)^{\alpha/2}\phi=u^2,\\lim_{|x|\to \infty}\phi(x)=0,&{\rm in}\ \mathbb{R}^3,\end{array}\right.}\) where \({\alpha \in (1,2]}\). Under certain assumptions, we obtain the existence of Nontrivial Solution of the above problem without compactness by using the methods of perturbation and the mountain pass theorem.
Juntao Sun - One of the best experts on this subject based on the ideXlab platform.
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existence of Nontrivial Solution for schrodinger poisson systems with indefinite steep potential well
Zeitschrift für Angewandte Mathematik und Physik, 2017Co-Authors: Juntao SunAbstract:In this paper, we study a class of nonlinear Schrodinger–Poisson systems with indefinite steep potential well: $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\Delta u+V_{\lambda }(x)u+K(x)\phi u=|u|^{p-2}u &{} \text { in }\mathbb {R}^{3},\\ -\Delta \phi =K\left( x\right) u^{2} &{} \ \text {in }\mathbb {R}^{3}, \end{array} \right. \end{aligned}$$ where $$3
Yangxin Yao - One of the best experts on this subject based on the ideXlab platform.
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existence of Nontrivial Solution for biharmonic problems involving critical sobolev exponents
南京師大學報（自然科學版）, 2007Co-Authors: Ahamed Adam Abdelgadir, Yaotian Shen, Yangxin YaoAbstract:It is proved that existence of a Nontrivial Solution for biharmonic problem involving a critical Sobolev exponent (The equation is abbreviated) where Ω is a bounded domain in R(superscript N) be a smooth bounded domain and (The equation is abbreviated) is the critical Sobolev exponent, u, v is the outer normal vector on ∂Ω, and f (x) is a given function. By using the variational principle, we prove the existence of Nontrivial Solution for biharmonic problem involving the critical Sobolev exponent.
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Nontrivial Solution for a class of semilinear biharmonic equation involving critical exponents
Acta Mathematica Scientia, 2007Co-Authors: Yangxin Yao, Rongxin Wang, Yaotian ShenAbstract:Abstract In this article, the authors prove the existence and the nonexistence of Nontrivial Solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.
