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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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