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Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a...

Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A...

This volume contains the notes of the lectures delivered at the CIME course GeometricAnalysis andPDEsduringtheweekofJune11 162007inCetraro (Cosenza). The school consisted in six courses held by M. Gursky (PDEs in Conformal Geometry), E. Lanconelli (Heat kernels in sub-Riemannian s- tings), A. Malchiodi(Concentration of solutions for some singularly perturbed Neumann problems), G. Tarantello (On some elliptic problems in the study of selfdual Chern-Simons vortices), X. J. Wang (Thek-Hessian Equation)and P. Yang (Minimal Surfaces in CR Geometry). Geometric PDEs are a ?eld of research which is...