Abstract
In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and theexistence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:−△u + u + ϕ(x)u = λ|u|p−1u, in R3,−△ϕ(x) = |u|2, in R3.By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy forsuch sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions areavailable in the literature. Our work generalize some results in literature.
Highlights
AND MAIN RESULTSIn this paper, we study the multiplicity of sign-changing solutions of the following nonlinear Schrödinger-Poisson system:u u (x)u | u |p 1 u, in 3, (1.1)(x) | u |2, on 3.where p (3,5), is a parameter
By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow, we prove that this system has infinitely many sign-changing solutions With the prescribed Lp 1- norm and has a least energy for such sign-changing restrained solution for p (3,5)
We study the multiplicity of sign-changing solutions of the following nonlinear Schrödinger-Poisson system:
Summary
We study the multiplicity of sign-changing solutions of the following nonlinear Schrödinger-Poisson system:. Where a suitable subset was given in which there exist two subsets separating the motivating functional, and on which an auxiliary operator A was constructed, so that we are able to apply suitable minimax arguments in the presence of invariant sets of a descending flow generated by the operator A to obtain the existence of multiple sign-changing solutions with restraint to system (1.1). We have used this method to obtain an analogous result to (1.1) for p (3,5) and 1. We prove Theorem 1.1 in section 3 and Theorem 1.2 in section 4, respectively
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