Existence of positive stationary solutions for a reaction-diffusion system

Abstract

In this paper, we will establish some existence results of positive stationary solutions for a reaction-diffusion systemThe main method used here is the well-known fixed point theorem of cone expansion and compression. MSC: 34B10

Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities

“…Meanwhile, some authors have also focused on the existence of positive solutions of the one-dimensional analogue of (1.3). See, for instance, Wang and An [7][8][9], Li [10], Chen [11,12], and references therein. However, as far as we know, most of papers mentioned are devoted to system (1.3) subject to Dirichlet boundary condition, which means that there is no neutron flux on the boundary of the container and the constant temperature on it, whereas the results associated with (1.4) are relatively rare.…”

Analysis on Existence of Positive Solutions for a Class Second Order Semipositone Differential Equations

“…have a strong physical meaning in quantum mechanics models [1,2], in semiconductor theory [3], or in a timeand space-dependent mathematical model of nuclear reactors in a closed container [4]. To the best of our knowledge, existence and multiplicity of nontrivial solutions of BVP (1) have been widely studied by using the variational method [5], bifurcation techniques [6,7], or fixed-point theorems [8][9][10][11]. In general, in order to ensure the positivity of the solutions of Equation (1), one of the crucial assumptions is that the nonlinearity f is nonnegative.…”