一类拟线性Kirchhoff型椭圆方程组多解的存在性

Abstract

Abstract:

In this paper, using Nehari manifold and fibering maps we study the existence of multiple nontrivial nonnegative solutions for the nonlocal quasilinear elliptic system

where Ω is a bounded smooth domain of R^N, △_pu=div (|▽u|^p-2▽u) is the p-Laplacian with 1 < p < N,α >1,β>1,α+β < p < p (k+1) < r < p^*(p^*=p^N/N-p if N>p,p^*=∞ if N ≤ p),λ,μ >0,h (x),g₁(x),g₂(x)∈C (Ω) are functions which change sign in Ω and M (s)=a+bs^k,a,b,k>0.

Key words: Quasilinear elliptic system, Nehari manifold, Fibering map, p-Laplacian

CLC Number:

O175.2

Chen Lin. Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type[J].Acta mathematica scientia,Series A, 2017, 37(4): 671-683.

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References

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Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type

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