System of nonlocal resonant boundary value problems involving p-Laplacian

Abstract

Abstract Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem ( φ ( x ′ ) ) ′ = f ( t , x , x ′ ) , x ′ ( 0 ) = 0 , x ( 1 ) = ∫ 0 1 x ( s ) d g ( s ) , $$\begin{array}{} \displaystyle (\varphi (x'))' =f(t,x,x'),\quad x'(0)=0, \quad x(1)=\int\limits_{0 }^{1}x(s){\rm d} g(s), \end{array}$$ where the function ϕ : ℝ n → ℝ n is given by ϕ (s) = (φ p1(s 1), …, φpn (sn )), s ∈ ℝ n , pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝ n × ℝ n → ℝ n is continuous and g : [0,1] → ℝ n is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.