Affiliation:
1. School of Mathematics and Statistics Xi'an Jiaotong University Xi'an Shaanxi China
2. Faculty of Applied Mathematics AGH University of Science and Technology Krakow Poland
3. Faculty of Electrical Engineering and Communication Brno University of Technology Brno Czech Republic
4. Department of Mathematics University of Craiova Craiova Romania
5. Simion Stoilow Institute of Mathematics of the Romanian Academy Bucharest Romania
6. School of Mathematics Zhejiang Normal University Jinhua China
Abstract
AbstractIn this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight,
where , , , , and is an indefinite sign weight which may admit non‐trivial positive and negative parts. Here, is the ‐Laplacian operator and is the weighted ‐Laplace operator defined by . The problem can be degenerate, in the sense that the infimum of in may be zero. Our main results distinguish between the cases and . In the first case, we establish the existence of a continuous family of eigenvalues, starting from the principal frequency of a suitable single phase eigenvalue problem. In the latter case, we prove the existence of a discrete family of positive eigenvalues, which diverges to infinity.
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Reference27 articles.
1. Eigenvalues of the indefinite‐weight p‐Laplacian in weighted spaces;Allegretto W.;Funkcial. Ekvac,1995
2. Nonlinear Analysis and Semilinear Elliptic Problems
3. Regularity for general functionals with double phase
4. A class of eigenvalue problems for the (p, q)‐Laplacian in RN$\mathbb {R}^N$;Benouhiba N.;Int. J. Pure Appl. Math.,2012
5. On the solutions of the -Laplacian problem at resonance