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Existence and multiplicity of solutions for degenerate \(p(x)\)-Laplace equations involving concave-convex type nonlinearities with two parameters. (English) Zbl 1360.35076
Summary: We show the existence of two nontrivial nonnegative solutions and infinitely many solutions for degenerate \(p(x)\)-Laplace equations involving concave-convex type nonlinearities with two parameters. By investigating the order of concave and convex terms and using a variational method, we determine the existence according to the range of each parameter. Some Caffarelli-Kohn-Nirenberg type problems with variable exponents are also discussed.

MSC:
35J70 Degenerate elliptic equations
35J62 Quasilinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B09 Positive solutions to PDEs
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
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