Nonhomogeneous boundary value problems in anisotropic Sobolev spaces

Abstract: We study the nonlinear boundary value problem in Ω, on ∂Ω, where is a bounded domain with smooth boundary, λ is a positive real number, and the continuous functions and q satisfy and for any and any . By analyzing the growth of the functions and q we prove in this Note several existence results in Sobolev spaces with variable exponents. To cite this article: M. Mihăilescu et al., C. R. Acad. Sci. Paris, Ser. I 345 (2007). [Copyright &y& Elsevier]