Ebook: Asymptotics of Nonlinearities and Operator Equations

New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.

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New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.

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New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.
Content:
Front Matter....Pages i-viii
Norm estimates for solutions of integral-functional inequalities....Pages 1-42
Two-sided estimates for nonlinearities....Pages 43-83
The use of arguments of leading eigenvalues....Pages 85-133
Weak nonlinearities....Pages 135-184
One-sided estimates for nonlinearities....Pages 185-266
Back Matter....Pages 267-278

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New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.
Content:
Front Matter....Pages i-viii
Norm estimates for solutions of integral-functional inequalities....Pages 1-42
Two-sided estimates for nonlinearities....Pages 43-83
The use of arguments of leading eigenvalues....Pages 85-133
Weak nonlinearities....Pages 135-184
One-sided estimates for nonlinearities....Pages 185-266
Back Matter....Pages 267-278
....