Francesco Nicolosi

Quasilinear elliptic equations with degenerations and singularities

Presents modern methods and techniques for solving boundary value problems for nonlinear elliptic operators. Focus is upon existence and bifurcation results in appropriate Sobolev spaces. The subject of this book is the theory of nonlinear boundary value problems for elliptic operators with degeneration and singularity. It focuses on the existence and bifurcation of weak solutions in appropriate weighted Sobolev spaces. The main tools are functional analytic methods based on the variational approach and the theory of topological degree of monotone type nonlinear mapping. Topics covered include: existence results for higher order boundary value problems in a rather general setting. An extensive study of the p-Laplacian and its degenerated and singular modifications, mainly existence and bifurcation results on bounded domains as well as on the whole Euclidean space. The text requires some basic knowledge of nonlinear functional analysis and differential equations. Elementary facts on function spaces and the theory of nonlinear operators are discussed in the first chapter.

Weak solutions of degenerated quasilinear elliptic equations of higher order

We prove the existence of weak solutions of higher order degenerated quasihnear elliptic equations The mmn tools are the degree theory for generahzed monotone mappings and mbeddlng theorems between weighted Sobolev spaces The strmghtforward use of these mbeddlngs allows us to consider more general assumpnons than those m our prece&ng paper (3)