Anisotropic problems with unbalanced growth

Advances in Nonlinear Analysis

article

Ahmed Alsaedi¹  Bashir Ahmad¹ 

[1] Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University

关键词: Nonlinear elliptic equation;    nonhomogeneous differential operator;    variable exponent;    weak solution;    mountain pass;   

DOI  :  10.1515/anona-2020-0063

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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 * ). The proof combines variational methods, analytic tools, and monotonicity arguments.

【 授权许可】

CC BY