Existence and nonexistence of global solutions for a semilinear reaction–diffusion system

Local and global nonexistence of solutions to semilinear evolution equations

For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u− V (x)u+ th(x)u +W (x, t), posed in ST := R × (0, T ), where 0 < T < +∞, (−∆) β 2 with 0 < β ≤ 2 is the β/2 fractional power of the −∆, and W (x, t) = tw(x) ≥ 0. The potential V satisfies lim sup|x|→+∞ |V (x)||x| < +∞, for some positive a...

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms

We consider the initial value problem for the reaction-diffusion system with inhomogeneous terms. In this paper we show the existence and nonexistence of global solution in time. Especially, for the nonexistence we extend the conditions of the nonlinear terms and the initial data to the weaker conditions. We prove that for the nonlinear term and the initial data whose support is included in som...

Existence and uniqueness of solutions for a semilinear elliptic system

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.

Existence and Nonexistence of Global Solutions of a Weakly Coupled System of Reaction-Diffusion Equations