Anisotropic problems with unbalanced growth
The main purpose of this paper is to study a general class of (p, q)-type eigenvalues problems with lack of compactness. The reaction is a convex-concave nonlinearity described by power-type terms. Our main result establishes a complete description of all situations that can occur. We prove the exis...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
De Gruyter
2020-03-01
|
Series: | Advances in Nonlinear Analysis |
Subjects: | |
Online Access: | https://doi.org/10.1515/anona-2020-0063 |
Summary: | The main purpose of this paper is to study a general class of (p, q)-type eigenvalues problems with lack of compactness. The reaction is a convex-concave nonlinearity described by power-type terms. Our main result establishes a complete description of all situations that can occur. We prove the existence of a critical positive value λ* such that the following properties hold: (i) the problem does not have any entire solution in the case of low perturbations (that is, if 0 < λ < λ*); (ii) there is at least one solution if λ = λ*; and (iii) the problem has at least two entire solutions in the case of high perturbations (that is, if λ > λ*). The proof combines variational methods, analytic tools, and monotonicity arguments. |
---|---|
ISSN: | 2191-9496 2191-950X |