Existence of ground state solutions to the nonlinear kirchho-type equations with potentials

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14 Citations (Scopus)

Abstract

In this paper, we study the existence of ground state solutions to the nonlinear Kirchho- type equations -m(||∇u||2 L2(RN)) Δu + V (x)u = |u|p-1u in RN; u ∈ H1(RN); N ≥ 1 where 1 < p < ∞ when N = 1; 2, 1 < p < (N + 2)=(N - 2) when N ≥ 3, m : [0,∞) → (0,∞) is a continuous function and V : RN → R a smooth function. Under suitable conditions on m(s) and V , it is shown that a ground state solution to the above equation exists.

Original languageEnglish
Pages (from-to)943-966
Number of pages24
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume35
Issue number3
DOIs
Publication statusPublished - 2015 Mar 1
Externally publishedYes

Keywords

  • Ground state solutions
  • Kirchho- type equations
  • Monotonicity trick
  • The Pohozaev identity
  • Variational methods

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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