Nonlinear elliptic problems involving the generalized p(u)-Laplacian operator with Fourier boundary condition

Said Ait Temghart; Chakir Allalou; Khalid Hilal

doi:10.5269/bspm.62948

Said Ait Temghart Sultan Moulay slimane University https://orcid.org/0000-0002-7962-2296
Chakir Allalou Sultan Moulay Slimane University https://orcid.org/0000-0002-4885-9397
Khalid Hilal Sultan Moulay slimane University

Abstract

This paper considers the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem with Fourier boundary conditions, when the variable exponent p is a real continuous function and we have dependency on the solution u. We get the results by assuming the right-hand side function f to be an integrable function, and by using the regularization approach combined with the theory of Sobolev spaces with variable exponents.

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