No abstract

No abstract

Using topological degree arguments, several existence theorems are proved for the following system of nonlocal resonant boundary value problem x = f (t, x, x), x (0) = 0, x (1) = 1 0 x (s) dg(s) where f : [0, 1] × R k × R k → R k is continuous and bounded, g = diag (g 1 ,. .. , g k)g j : [0, 1] → R has bounded variation (j = 1,. .. , k).

This paper deals with the existence of solutions for a system of equations ὔὔ = ( , , ὔ ), where : [0, 1] × ℝ × ℝ → ℝ is a vector function, subject to various nonlocal boundary conditions. The method is to impose an a priori bound condition on and apply the Leray-Schauder xed point theorem. Our results extend some results in the references and also provide the information on the existence of stationary solutions for the heat equation with nonlinear gradient source terms.