Critical Neumann Problem with Competing Hardy Potentials

Critical Neumann Problem with Competing Hardy Potentials

In this paper we investigate the solvability of the nonlinear Neumann problem (1) involving a critical Sobolev nonlinearity and two competing Hardy potentials in a bounded domain. We examine the common effect of the shape of the graph of the weight function, the mean curvature of the boundary and Ha...

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Journal Title: Revista Matemática Complutense
First author: Jan Chabrowski
Other Authors: Daomin Cao
Traslated keyword:
Language: Undetermined
Get full text: https://revistas.ucm.es/index.php/REMA/article/view/REMA0707220309A
Resource type: Journal Article
Source: Revista Matemática Complutense; Vol 20, No 2 (Year 2007).
DOI: http://dx.doi.org/10.5209/rev_REMA.2007.v20.n2.16485
Publisher: Universidad Complutense de Madrid
Usage rights: Cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de los editores. 
Categories: Physical/Engineering Sciences --> Mathematics
Physical/Engineering Sciences --> Mathematics, Applied
Abstract: In this paper we investigate the solvability of the nonlinear Neumann problem (1) involving a critical Sobolev nonlinearity and two competing Hardy potentials in a bounded domain. We examine the common effect of the shape of the graph of the weight function, the mean curvature of the boundary and Hardy potentials on the existence of solutions of problem (1). We are mainly interested in the existence of positive solutions. We also obtain the existence of sign-changing solutions.