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Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator
Authors:Claudianor?O.?Alves  author-information"  >  author-information__contact u-icon-before"  >  mailto:coalves@dme.ufcg.edu.br"   title="  coalves@dme.ufcg.edu.br"   itemprop="  email"   data-track="  click"   data-track-action="  Email author"   data-track-label="  "  >Email author,Alannio?B.?Nóbrega
Affiliation:1.Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática,Campina Grande,Brazil
Abstract:
Using variational methods, we establish existence of multi-bump solutions for the following class of problems
$$begin{aligned} left{ begin{array}{l} Delta ^2 u +(lambda V(x)+1)u = f(u), quad text{ in } quad mathbb {R}^{N}, u in H^{2}(mathbb {R}^{N}), end{array} right. end{aligned}$$
where (N ge 1), (Delta ^2) is the biharmonic operator, f is a continuous function with subcritical growth, (V : mathbb {R}^N rightarrow mathbb {R}) is a continuous function verifying some conditions and (lambda >0) is a real constant large enough.
Keywords:
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