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On the Fredholm-type theorems and sign properties of solutions for \((p, q)\)-Laplace equations with two parameters. (English) Zbl 1435.35183
The authors consider the Dirichlet problem for the nonhomogeneous \((p,q)\)-Laplacian equation in a bounded domain in \(\mathbb{R}^N\), \(N\geq 1\). Three existence and multiplicity theorems and two sign property results for the solutions are proved using variational methods. The proofs are complete and nonstandard. They are based on interesting energy estimates and linking arguments.
MSC:
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J20 Variational methods for second-order elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35B50 Maximum principles in context of PDEs
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