Multiple solutions for a nonhomogeneous Schrodinger-Poisson system with concave and convex nonlinearities |
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| Authors: | Lixia Wang and Shiwang Ma |
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| Institution: | Center for Applied Mathematics, Tianjin University, Weijin Road, Tianjin, China,School of Mathematical Sciences and LPMC, Nankai University, Weijin Road, Tianjin, China |
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| Abstract: | In this paper, we consider the following nonhomogeneous Schrodinger-Poisson equation
$$
\left\{
- \Delta u +V(x)u+\phi(x)u =-k(x)|u|^{q-2}u+h(x)|u|^{p-2}u+g(x), &x\in \mathbb{R}^3,\\ \Delta \phi =u^2, \quad \lim_{|x|\rightarrow +\infty}\phi(x)=0, & x\in \mathbb{R}^3,
\right.
$$
where $1
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| Keywords: | Schrodinger-Poisson systems concave and convex nonlinearities variational methods Ekeland''s variational principle Mountain Pass Theorem |
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