pith. machine review for the scientific record. sign in

arxiv: 1510.01409 · v3 · submitted 2015-10-06 · 🧮 math.AP

Recognition: unknown

Multi-bump solutions for Choquard equation with deepening potential well

Authors on Pith no claims yet
classification 🧮 math.AP
keywords equationlambdamulti-bumpomegasolutionsarraychoquardparameter
0
0 comments X
read the original abstract

We study the existence of multi-bump solutions to Choquard equation $$ \begin{array}{ll} -\Delta u + (\lambda a(x)+1)u=\displaystyle\big(\frac{1}{|x|^{\mu}}\ast |u|^p\big)|u|^{p-2}u \mbox{ in } \,\,\, \R^3, \end{array} $$ where $\mu \in (0,3), p\in(2, 6-\mu)$, $\lambda$ is a positive parameter and the nonnegative function $a(x)$ has a potential well $ \Omega:=int (a^{-1}(0))$ consisting of $k$ disjoint bounded components $ \Omega:=\cup_{j=1}^{k}\Omega_j$. We prove that if the parameter $\lambda$ is large enough then the equation has at least $2^{k}-1$ multi-bump solutions.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.