New multiple solutions for a Schrödinger-Poisson system involving concave-convex nonlinearities

Authors : Chun-yu LEI, Gao-sheng LIU, Chang-mu CHU, Hong-mın SUO

Pages : 986-997

Doi:10.3906/mat-1807-100

View : 11 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we study the following critical growth Schr¨odinger–Poisson system with concave-convex nonlinearities term { −∆u + u + ηφu = λf x u q−1 + u 5 , in R 3 , −∆φ = u 2 , in R 3 , 0.1 where 1 0 is a real parameter and f ∈ L 6 6−q R 3 is a nonzero nonnegative function. Using the variational method, we obtain that there exists a positive constant λ∗ > 0 such that for all λ ∈ 0, λ∗ , the system has at least two positive solutions.
Keywords : Schrödinger Poisson system, critical exponent, concave convex nonlinearities