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\(p(x)\)-Laplacian equations in \(\mathbb R^N\) with periodic data and nonperiodic perturbations. (English) Zbl 1135.35034

Summary: We consider the \(p(x)\)-Laplacian equations in \(\mathbb R^N\) with periodic data and nonperiodic perturbations being stationary at infinity, where the perturbations are done not only for the coefficients but also for the exponents. Using concentration-compactness principle, under appropriate assumptions, we prove the existence of ground state solutions vanishing at infinity for the equations.

MSC:

35J60 Nonlinear elliptic equations
35B20 Perturbations in context of PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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