Weak Convergence Methods for Semilinear Elliptic Equations

By: Jan Chabrowski

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Hardcover | 1 December 1999

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248 Pages

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22.23 x 15.88 x 1.91

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This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrodinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais-Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration-compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik-Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions.

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Differential Calculus & Equations Topology Algebraic Topology Booktopia Publisher Services World Scientific Publishing

Preface
Concentration-compactness principle at infinity	p. 1
Constrained minimization	p. 21
Nonlinear eigenvalue problem	p. 67
Artificial constraints	p. 89
Inverse power method	p. 119
Effect of topology	p. 135
Multi-peak solutions	p. 159
Multiple positive and nodal solutions	p. 205
Bibliography	p. 225
Index	p. 233
Table of Contents provided by Blackwell. All Rights Reserved.

Weak Convergence Methods for Semilinear Elliptic Equations

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