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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 nonlinear driving forces f = f ( t, x, u), as well as nonlinear external damping terms Q = Q( t, x, u, u t), both of which could significantly dependent on the time t. The theorems are obtained through the study of the natural energy Eu associated to the solutions u of the systems. Thanks to a new approach of the classical potential well and concavity methods, we show the nonexistence of global solutions, when the initial energy is controlled above by a critical value; that is, when the initial data belong to a specific region in the phase plane. Several consequences, interesting in applications, are given in particular subcases. The results are original also for the scalar standard wave equation when p ≡ 2 and even for problems linearly damped. [ABSTRACT FROM AUTHOR]

Non-existence results for non-negative distribution entire solutions of singular quasilinear elliptic differential inequalities with weights are established. Such inequalities include the capillarity equation with varying gravitational field h, as well as the general p-Poisson equation of radiative cooling with varying heat conduction coefficient g and varying radiation coefficient h. Since we deal with inequalities and positive weights, it is not restrictive to assume h radially symmetric. Theorem 1 extends in several directions previous results and says that solely entire large solutions can exist, while Theorem 2 shows that in the p-Laplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest. [ABSTRACT FROM AUTHOR]

A correction to the article "Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights" which appeared in an issue of "Archives of Rational Mechanical Analysis" is presented.