Abstract
Abstract We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a negative sign and of an asymmetric asymptotically linear term which is resonant in the negative direction. Using variational methods together with truncation and perturbation techniques and Morse theory (critical groups), we prove two multiplicity theorems producing four and five, respectively, nontrivial smooth solutions when the parameter λ > 0 {\lambda>0} is small.
Highlights
Let Ω ⊆ RN be a bounded domain with a C 2 -boundary ∂Ω
In this paper we study the following parametric Robin problem: (
Note that in our problem the concave nonlinearity enters with a negative sign
Summary
Let Ω ⊆ RN be a bounded domain with a C 2 -boundary ∂Ω. In this paper we study the following parametric Robin problem:. In the reaction we have the competing effects of resonant and concave terms. Note that in our problem the concave nonlinearity enters with a negative sign. Such problems were considered by Perera [12], de Paiva & Massa [6], de Paiva & Presoto [7] for Dirichlet problems with zero potential (that is, ξ ≡ 0). Only de Paiva & Presoto [7] have an asymmetric reaction of special form, which is superlinear in the positive direction and linear and nonresonant in the negative direction. Indefinite and unbounded potential, concave term, asymmetric reaction, critical groups, multiple solutions, Harnack inequality. Our approach uses variational tools based in the critical point theory, together with suitable truncation, perturbation and comparison techniques and Morse theory (critical groups)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
