This 2003 book presents min-max methods through a study of the different faces of the
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …

The paper deals with local and global existence for the solutions of the wave equation in
bounded domains with nonlinear boundary damping and source terms. The typical problem …

In this paper we consider the problem of non-continuation of solutions of dissipative
nonlinear Kirchhoff systems, involving the p (x)-Laplacian operator and governed by …

This paper is concerned with the study of the nonlinearly damped system of wave equations
with Dirichlét boundary conditions: utt−∆ u+| ut| m− 1ut= Fu (u, v) in Ω×(0,∞), vtt−∆ v+| vt| r …

We consider finite energy solutions of a wave equation with supercritical nonlinear sources
and nonlinear damping. A distinct feature of the model under consideration is the presence …

The paper deals with local existence, blow-up and global existence for the solutions of a
wave equation with an internal nonlinear source and a nonlinear boundary damping. The …

This paper is concerned with the study of the nonlinear damped wave equation u_ tt-Δ u+ h
(u_t)= g (u)\quad\rm in\, Ω * 0, ∞, where Ω is a bounded domain of R^ 2 having a smooth …

In mathematical physics we increasingly encounter PDEs models connected with vibration
problems for elastic bodies and deformation processes, as it happens in the Kirchhoff–Love …

The aim of this paper is to study the problem\left {u_ tt-Δ u+ P (x, u_t)= f (x, u)\quad &\rm
in\,(0, ∞) * Ω,\u= 0 &\rm on\,(0, ∞) *\Gamma_0,\u_ tt+\partial_ ν u-\Delta_ Γ u+ Q (x, u_t)= g …

This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u tt− Δ pu−
Δu t= f (u), in a bounded domain Ω⊂ ℝ 3 and subject to Dirichlét boundary conditions. The …