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.
Highlights
We study the existence and multiplicity of solutions for a Ni-Serrin type equation involving non-standard growth condition and arising from capillarity phenomena of the following type:
+|∇ u| p(x) where ⊂ RN is a bounded domain with sm√ooth boundary ∂, p ∈ C( ) such that
Capillarity can be briefly explained by considering the effects of two opposing forces: adhesion, i.e., the attractive force between the molecules of the liquid and those of the container; and cohesion, i.e., the attractive force between the molecules of the liquid
Summary
We study the existence and multiplicity of solutions for a Ni-Serrin type equation involving non-standard growth condition and arising from capillarity phenomena of the following type:. Capillarity can be briefly explained by considering the effects of two opposing forces: adhesion, i.e., the attractive (or repulsive) force between the molecules of the liquid and those of the container; and cohesion, i.e., the attractive force between the molecules of the liquid. The study of capillary phenomena has gained some attention recently. This increasing interest is motivated by fascination in naturally-occurring phenomena such as motion of drops, bubbles and waves and its importance in applied fields ranging from industrial and biomedical and pharmaceutical to microfluidic systems
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