Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions

作者：Nguyen Thanh Chung^*; Ngo Quoc Anh

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2010, 140(2): 259-272.

DOI：10.1017/s030821050800070x

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(vertical bar del u vertical bar(p(x)-2)del u) + vertical bar u vertical bar(p(x)-2)u = 0 in Omega,
vertical bar del u vertical bar(p(x)-2)partial derivative u/partial derivative n = lambda g(x, u) on partial derivative Omega,
where Omega is a bounded domain with smooth boundary, n is the outer unit normal to partial derivative Omega and lambda is a parameter. Furthermore, we want to emphasize that g : partial derivative Omega x [0, infinity) -> R is a continuous function that may or may not satisfy the Ambrosetti-Rabinowitz-type condition.

• 出版日期2010