Two solutions for an elliptic equation with fast increasing weight and concave-convex nonlinearities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Furtado, Marcelo F.¹  Ruviaro, Ricardo¹  da Silva, Joao Pablo P.² 

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Fed Univ Para, Dept Matemat, BR-66075110 Belem, PA, Brazil

关键词: Elliptic equations;    Combined nonlinearities;    Critical problems;    Variational methods;   

DOI  :  10.1016/j.jmaa.2014.02.068

来源: Elsevier

【 摘 要 】

We prove the existence of two nonnegative nontrivial solutions for the equation -div(K(x)del u) = a(x)K (x)vertical bar u vertical bar(q-2)u + b(x)K (x)vertical bar u vertical bar(p-2)u, x epsilon R-N, where N >= 3, K(x) = exp(vertical bar x vertical bar(alpha)/4), alpha >= 2 and the potentials a and b have indefinite sign and satisfy some mild integrability conditions. The results hold when a has small norm in a suitable weighted Lebesgue space. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free