Turkish Journal of Mathematics
Abstract
In this paper, we study the following critical growth Schrödinger-Poisson system with concave-convex nonlinearities term $\left\{\begin{array} -\Delta u + u + \eta\varphi u = \lambda f(x) u^{q-1} + u^5, in R^3, \\ -\Delta \varphi = u^2, in R^3,\end{array}\right. $ where $1 < q < 2, \eta\in \mathbb{R}, \lambda > 0$ is a real parameter and $f \in L^{\frac{6}{6-q}} (\mathbb{R}^3)$ is a nonzero nonnegative function. Using the variational method, we obtain that there exists a positive constant $\lambda_* > 0$ such that for all $\lambda \in (0,\lambda_*)$, the system has at least two positive solutions.
DOI
10.3906/mat-1807-100
Keywords
Schrödinger-Poisson system, critical exponent, concave-convex nonlinearities
First Page
986
Last Page
997
Recommended Citation
LEI, C, LIU, G, CHU, C, & SUO, H (2020). New multiple solutions for a Schrödinger-Poisson system involving concave-convex nonlinearities. Turkish Journal of Mathematics 44 (3): 986-997. https://doi.org/10.3906/mat-1807-100
