Multi-bump solutions for Choquard equation with deepening potential well

By Claudianor Oliveira Alves, Alânnio B. Nóbrega, Minbo Yang. 2015

160 citations recorded by the source corpus.

In this paper we study the existence of multi-bump solutions for the following Choquard equation $$\begin{aligned} \begin{array}{ll} -\Delta u + (\lambda a(x)+1)u=\displaystyle \big (\frac{1}{|x|^{\mu }}*|u|^p\big )|u|^{p-2}u \text{ in } \,\,\, \mathbb {R}^3, \end{array} \end{aligned}$$-Δu+(λa(x)+1)u=(1|x|μ∗|u|p)|u|p-2uinR3,where $$\mu \in (0,3), p\in (2, 6-\mu )$$μ∈(0,3),p∈(2,6-μ), $$\lambda $$λ is a positive parameter and the nonnegative continuous function a(x) has a potential well $$ \Omega :=int (a^{-1}(0))$$Ω:=int(a-1(0)) which possesses k disjoint bounded components $$ \Omega :=\cup _{j=1}^{k}\Omega _j$$Ω:=∪j=1kΩj. We prove that if the parameter $$\lambda $$λ is large enough, then the equation has at least $$2^{k}-1$$2k-1 multi-bump solutions.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/87abe66a5b286a0f4a7d8f0f10d94d0a36443de8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

  1. Fashun Gao
  2. Minbo Yang
  3. Xinfu Li
  4. Daniele Cassani
  5. Jianjun Zhang

In Control and Systems Engineering

  1. Fashun Gao
  2. Minbo Yang

In Mathematical Physics

  1. Fashun Gao
  2. Minbo Yang
  3. Xinfu Li

Citations in the corpus