Laplacian type quasilinear elliptic equations nonlinear boundary conditions
Issue Date:
2010
Publisher:
Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Citation:
Volume: 140, Issue: 2, Page : 259-272
Abstract:
Using variational methods we study the non-existence and multiplicity of non-negative solutions
for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions of the
form -Div(|?? u|p(x)-2??u)+|u|p(x)-2u=0 in ?? |?? u|p(x)-2\??u\?? n =? g(x,u) on ?? ?? where ?? is a bounded
domain with smooth boundary, n is the outer unit normal to ?? ?? and ? is a parameter. Furthermore, we
want to emphasize that g: ?? ?? ?? [0,??) ?? ? is a continuous function that may or may not satisfy the
Ambrosetti-Rabinowitz-type condition. ?? 2010 Royal Society of Edinburgh.
