### A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations

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The existence of classical solutions for some partial differential equations on tori is shown.

We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a replacement lemma which has as a corollary a maximum principle for minimizers.

The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in $3$D.

This paper is concerned with the existence of positive solutions of a multi-point boundary value problem for higher-order differential equation with one-dimensional $p$-Laplacian. Examples are presented to illustrate the main results. The result in this paper generalizes those in existing papers.

A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.