A weighted (p,2)-equation with double resonance

[摘要] We consider a Dirichlet problem driven by a weighted (p,2)-Laplacian with a reaction which is resonant both at\(\pm\infty\)and at zero(double resonance). We prove a multiplicity theorem producing three nontivial smoothsolutions with sign information and ordered.In the Appendix we develop the spectral properties of the weighted r-Laplace differential operator.

[学科分类] 数学（综合）

[关键词] Constant sign and nodal solutions;nonlinear regularity;nonlinear maximum principle;critical groups;spectrum of weighted r-Laplacian;double resonance.