Abstract
In this paper, we apply the methods of Nehari manifold to study a class of Schrödinger–Poisson system in a bounded domain \(\Omega \subset {\mathbb R}^3\) submitted to Dirichlet boundary conditions. Under a general 4-superlinear conditions on the nonlinearity f, we prove the existence of a ground state solution. In case the nonlinearity f is odd with respect to the second variable, we obtain the existence of infinitely many solutions. In the proofs, the Nehari manifold does not need to be of \(C^1\) class.
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This work was supported by National Natural Science Foundation of China (Grant Nos. 11371212, 10601063, 11271386).
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Ba, Z., He, X. Solutions for a class of Schrödinger–Poisson system in bounded domains. J. Appl. Math. Comput. 51, 287–297 (2016). https://doi.org/10.1007/s12190-015-0905-7
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DOI: https://doi.org/10.1007/s12190-015-0905-7