Perturbations of Lane-Emden and Hamilton-Jacobi equations II: Exterior domains

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Ai, Shangbing¹  Cowan, Craig² 

[1] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

关键词: Linearized operators;    Entire solutions;    Lane-Emden;    Nonlinear gradient;    Exterior domains;   

DOI  :  10.1016/j.jde.2016.02.012

来源: Elsevier

【 摘 要 】

In this article we are interested in the existence of positive classical solutions of and {-Delta u + a(x) . del u + V(x)u = u(p) + gamma u(q) in Omega u = 0 on partial derivative Omega, (1) and {-Delta u + a(x) . del u + V(x)u = u(p) + gamma vertical bar del u vertical bar(q) in Omega u = 0 on partial derivative Omega, (2) where Omega is a smooth exterior domain in R-N in the case of N >= 4, p > N+1/N-3 and gamma is an element of R. We assume that V is a smooth nonnegative potential and a (x) is a smooth vector field, both of which satisfy natural decay assumptions. Under suitable assumptions on q we prove the existence of an infinite number of positive classical solutions. We also consider the case of N+2/N-2 < p < N+1/N-3 under further symmetry assumptions on Omega, a and V. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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