Abstract
The aim of this paper is to prove the existence of weak periodic solution and super solution for M×M reaction diffusion system with L1 data and nonlinearity on the gradient. The existence is proved by the technique of sub and super solution and Schauder fixed point theorem.
Highlights
]0, T [×∂Ω, −∆ denotes the Laplacian operator on L1(Ω) with Dirichlet boundary conditions, dj are positive constants, Gj is a caratheodory function and fj is a nonnegative measurable function belongs to
The goal of this paper is to investigate the case when the data are irregular and the nonlinearity has critical growth with respect to the gradient
Before showing the main result, we have to clarify in which sense we want to solve the system (1.1), for which we introduce the notion of weak periodic solution
Summary
We present two existence results for quasilinear parabolic periodic systems. The first result prove the existence when the nonlinearities are bounded by function L1. The second result concerns periodic systems with critical growth nonlinearity with respect to the gradient. Let us introduce the hypothesies which we assume throughout this section
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