Schrodinger-Kirchhoff-Poisson type systems

2015/03/25 by Cyril J. Batkam, Batkam, Cyril J., Joao R. Santos Junior +1
Mathematics · #35B33 #35J20 #35J25 #35J47 #35J50 #35J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B33 #msc:35J20 #msc:35J25 #msc:35J47 #msc:35J50 #msc:35J65

paper · pdf · doi:10.48550/arxiv.1503.07280

arxiv created 2015/03/25 · arxiv updated 2015/03/26

Abstract

In this article we study the existence of solutions to the system \ -(a+b∫_Ω|∇ u|²)Δu +ϕu= f(x, u) · in Ω\hbox -Δϕ= u² · in Ω\hbox u=ϕ=0 · on ∂Ω, \hbox . where Ω is a bounded smooth domain of ℝ^N (N=1,2 or 3), a>0, b≥0, and f:Ω× ℝ→ℝ is a continuous function which is 3-superlinear. By using some variants of the mountain pass theorem established in this paper, we show the existence of three solutions: one positive, one negative, and one which changes its sign. Furthermore, in case f is odd with respect to u we obtain an unbounded sequence of sign-changing solutions.

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