Nonlinear Problems with Lack of Compactness

Giovanni Molica Bisci; Patrizia Pucci

Published by De Gruyter 2021

Nonlinear Problems with Lack of Compactness

Giovanni Molica Bisci and Patrizia Pucci

Volume 36 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110652017

Overview
Contents

About this book

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.

An authoritative monograph on nonlinear and geometric analysis
Covers nonlinear problems in the Euclidean setting as well as on manifolds
Presents in detail the variational point of view

Author / Editor information

Giovanni Molica Bisci, University of Urbino Carlo Bo, Italy; Patrizia Pucci, University of Perugia, Italy.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	IX
Introduction Publicly Available Download PDF	XI
Part I: Elliptic equations in ℝ_Nwith nonstandard growth
1 Critical quasilinear equations of Marcellini’s type Requires Authentication Unlicensed Licensed Download PDF	3
2 On (p, N) Laplacian equations in ℝ^N with exponential nonlinearities Requires Authentication Unlicensed Licensed Download PDF	21
3 Critical Hardy–Kirchhoff equations in ℝ^N Requires Authentication Unlicensed Licensed Download PDF	43
Part II: Existence of multiple solutions via group-theoretical invariance in the Hilbertian setting
4 Multiple solutions for critical equations in ℝ^N Requires Authentication Unlicensed Licensed Download PDF	65
5 Weak solutions of a scalar field equation Requires Authentication Unlicensed Licensed Download PDF	85
6 Elliptic equations on the sphere Requires Authentication Unlicensed Licensed Download PDF	111
Part III: Variational Principles in Geometric Analysis
7 Subelliptic problems on Carnot groups Requires Authentication Unlicensed Licensed Download PDF	145
8 Arbitrarily many solutions on homogeneous Hadamard manifolds Requires Authentication Unlicensed Licensed Download PDF	173
9 Kirchhoff problems on the Poincaré ball model Requires Authentication Unlicensed Licensed Download PDF	203
A Appendix – the symmetric criticality principle Requires Authentication Unlicensed Licensed Download PDF	241
List of symbols Requires Authentication Unlicensed Licensed Download PDF	247
Bibliography Requires Authentication Unlicensed Licensed Download PDF	249
Index Requires Authentication Unlicensed Licensed Download PDF	261

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in mathematical analysis and partial differential equations.
Pages
- Front matter: 24
- Main content: 266
Illustrations
- Illustrations: 3
- Coloured Illustrations: 26
Keywords: Carnot-Gruppe; Geometrische Analysis; Nichtlineare Funktionalanalysis; Nichtlineare partielle Differentialgleichung; Variationsrechnung

eBook

Published: February 8, 2021
ISBN: 9783110652017

Hardcover

Published: February 8, 2021
ISBN: 9783110648867