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Open Access Research

Ni-Serrin type equations arising from capillarity phenomena with non-standard growth

Mustafa Avci

Author Affiliations

Department of Mathematics, Faculty of Science, Dicle University, Diyarbakir, 21280, Turkey

Boundary Value Problems 2013, 2013:55  doi:10.1186/1687-2770-2013-55

Published: 18 March 2013

Abstract

In the present paper, in view of the variational approach, we discuss a Ni-Serrin type equation involving non-standard growth condition and arising from the capillarity phenomena. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

MSC: 35D05, 35J60, 35J70.

Keywords:
<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/55/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/55/mathml/M1">View MathML</a>-Laplacian; variable exponent Sobolev space; mountain pass theorem; genus theory; variational method; capillarity phenomena