Nonlinear second order equations with applications to partial differential equations. (English) Zbl 0572.34004

In this paper we study the Cauchy problem for the abstract second order (in time) semilinear differential equation \(u''(t)+Au'(t)+Bu(t)=f(t,u(t))\) where A and B are linear operators in a Banach space. Then we use the abstract results that we obtained together with energy estimates and the center manifold theorem to study in concrete cases, global existence, stability and bifurcation of solutions of certain parabolic and hyperbolic equations.


34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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