Infinitely Many Solutions of Schrödinger‐Poisson Equations with Critical and Sublinear Terms

Xianzhong Yao, Xia Li, Fuchen Zhang and Chunlai Mu

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

Abstract: In this paper, we study the following Schrödinger‐Poisson equations −Δu+u+ϕu=u5+λaxup−1u,x∈ℝ3,−Δϕ=u2,x∈ℝ3, where the parameter λ > 0 and p ∈ (0, 1). When the parameter λ is small and the weight function a(x) fulfills some appropriate conditions, we admit the Schrödinger‐Poisson equations possess infinitely many negative energy solutions by using a truncation technology and applying the usual Krasnoselskii genus theory. In addition, a byproduct is that the set of solutions is compact.

Date: 2019
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https://doi.org/10.1155/2019/8453176

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:8453176

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