- Turkish Journal of Mathematics
- Vol: 44 Issue: 3
- New multiple solutions for a Schrödinger-Poisson system involving concave-convex nonlinearities
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 : 8 | Download : 3
Publication Date : 9999-12-31
Article Type : Makaleler
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