Abstract
In general, the existence of nodal solution for Schrödinger–Poisson systems with the nonlinearity f(x)|u|p−2u(4≤p<6) in R3 can be established by using the nodal Nehari manifold method. However, for the case where 2<p<4, such an approach is not applicable because Palais-Smale sequences restricted on the nodal Nehari manifold can be not bounded. In this paper, we introduce a novel constraint method to prove the existence of nodal solution to a class of non-autonomous Schrödinger–Poisson systems in the case where 2<p<4. We conclude that such solution changes sign exactly once in R3 and is bounded in H1(R3)×D1,2(R3). Moreover, the existence of least energy nodal solution is obtained in the case where 1+733<p<4, which remains unsolved in the existing literature.
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