Multiple positive solutions for a Schr\"odinger-Poisson-Slater system
By Gaetano Siciliano. 2009
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In this paper we investigate the existence of positive solutions to the following Schr\"odinger-Poisson-Slater system [c]{ll} - \Delta u+ u + \lambda\phi u=|u|^{p-2}u & \text{in} \Omega -\Delta\phi= u^{2} & \text{in} \Omega u=\phi=0 & \text{on} \partial\Omega. where $\Omega$ is a bounded domain in $\mathbf{R}^{3},\lambda$ is a fixed positive parameter and $p<2^{*}=\frac{2N}{N-2}$. We prove that if $p$ is "near" the critical Sobolev exponent $2^*$, then the number of positive solutions is greater then the Ljusternik-Schnirelmann category of $\Omega$.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/447726718f307b68ac59a1162e88b91c24c8517e
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In Applied Mathematics
In Computational Theory and Mathematics
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Citations in the corpus
- Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equations (2013, background): “, has been widely established, see [2, 3, 14, 18, 22, 23, 27] and the references therein. In particular, previous results on the multiplicity of solutions to (Eλ) have also been obtained. We refer to [1, 4, 13, 24] and their references in that direction. In those references, solutions are obtained a”