A Class of Operator Equations in Nonlinear Mechanics

Abstract

Abstract A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.” AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15. †Supported in part by the German Academic Exchange Service (DAAD) under its program “Studienaufenthalte auslaändischer Wissenschaftler.“ †Supported in part by the German Academic Exchange Service (DAAD) under its program “Studienaufenthalte auslaändischer Wissenschaftler.“ Notes †Supported in part by the German Academic Exchange Service (DAAD) under its program “Studienaufenthalte auslaändischer Wissenschaftler.“