Abstract
Using the variational method, we prove theexistence and multiplicity of solutions for a Steklov problem involving the $p(x)$-Laplacian-like operator, originated from a capillary phenomena. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained.
Publisher
Sociedade Paranaense de Matemática
Reference20 articles.
1. A. Boukhsas, B. Ouhamou, Steklov eigenvalues problems for generalized (p, q)-Laplacian type operators. To appear.
2. D.G. Costa, An Invitation to Variational Methods in Differential Equations. Birkhauser, Basel (2007)
3. P. Clement, R. Manasevich and E. Mitidieri, On a modified capillary equation, Journal of Differential Equations 124 (1996), 343-358.
4. D.E. Edmunds, J. Rakosnık, Sobolev embedding with variable exponent. Stud. Math. 143, 267-293 (2000).
5. D.E. Edmunds, J. Lang, A. Nekvinda, On Lp(x)(Ω) norms. Proc. R. Soc. Ser. A. 455, 219-225 (1999)