Asymptotics of Nonlinearities and Operator Equations

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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.