Molica Bisci G., Pucci P. Nonlinear Problems with Lack of Compactness

Berlin: de Gruyter, 2021. — 290 p.This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.Preface
Introduction
Elliptic equations in ℝ N with nonstandard growth
Critical quasilinear equations of Marcellini’s type
On (p, N) Laplacian equations in ℝN with exponential nonlinearities
Critical Hardy–Kirchhoff equations in ℝN
Existence of multiple solutions via group-theoretical invariance in the Hilbertian setting
Multiple solutions for critical equations in ℝN
Weak solutions of a scalar field equation
Elliptic equations on the sphere
Variational Principles in Geometric Analysis
Subelliptic problems on Carnot groups
Arbitrarily many solutions on homogeneous Hadamard manifolds
Kirchhoff problems on the Poincaré ball model
Appendix – the symmetric criticality principle
List of symbols
Bibliography
Index