Abstract
In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity f. Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness.
Highlights
Introduction and Main ResultsCitation: Lian, C.-B.; Zhang, B.-L.; Ge, B
Motivated by the papers mentioned above, in this work we study the existence of solutions for problem ( Pλ,μ ) in which the function f is assumed to be subcritical growth condition
The main results of this paper are as follow pS
Summary
With the aid of variational methods, we establish the existence and multiplicity results for a class of singular elliptic problems, involving a double phase operator, subject to Dirichlet boundary conditions in a smooth bounded domain in R N. The authors in [13] proved the existence and multiplicity of weak solutions of problem ( P1,0 ). Based on a direct sum decomposition of a space, Ge and Chen in [11] proved the existence of infinitely many solutions when the nonlinear term has a q − 1-superlinear growth at infinity and its primitive can be sign-changing. Motivated by the papers mentioned above, in this work we study the existence of solutions for problem ( Pλ,μ ) in which the function f is assumed to be subcritical growth condition. We complete the proofs of Theorems 1 and 2 in Sections 4 and 5, respectively
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