The existence of infinitely many solutions for a Dirichlet problem involving the p(x)-Laplacian is established. In our main result, under an appropriate oscillating behaviour of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Further, some applications and examples are pointed out. In particular, an existence result of infinitely many solutions for a two-point boundary value problem involving the variable exponent is presented. The approach is based on variational methods.

Existence results of infinitely many solutions for p(x)-Laplacian elliptic Dirichlet problems

BONANNO, Gabriele;CHINNI', Antonia
2012-01-01

Abstract

The existence of infinitely many solutions for a Dirichlet problem involving the p(x)-Laplacian is established. In our main result, under an appropriate oscillating behaviour of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Further, some applications and examples are pointed out. In particular, an existence result of infinitely many solutions for a two-point boundary value problem involving the variable exponent is presented. The approach is based on variational methods.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/2354821
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