An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains

2013/05/09 by Kanishka Perera, Perera, Kanishka, Patrizia Pucci +3
Mathematics · #35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35J66 #Secondary 35J70 #math.AP #msc:35J20 #msc:35J66 #msc:35J70

paper · pdf · doi:10.48550/arxiv.1305.2031

arxiv created 2013/05/09 · arxiv updated 2013/05/10

Abstract

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p-Laplacian operator and subcritical nonlinearities satisfying Ambrosetti-Rabinowitz type conditions. Using Morse theory and a cohomological local splitting as in Degiovanni et al. [5], we prove the existence of a nontrivial weak solution for all (real) values of the eigenvalue parameter. Our result is new even in the semilinear case p = 2 and complements some recent results obtained in Autuori et al. [1].

Related

• Existence and uniqueness for a quasilinear elliptic problem with nonlinear Robin conditions
• Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions
• Quasilinear elliptic and parabolic Robin problems on Lipschitz domains
• Existence problems for the p-Laplacian
• Bifurcation results for nonlinear eigenvalue problems involving the (p,q)-Laplace operator