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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)=∫01x(s)dg(s), $$\begin{array}{} \displaystyle (\varphi (x'))' =f(t,x,x'),\quad x'(0)=0, \quad x(1)=\int\limits_{0 }^{1}x(s){\rm… Click to show full abstract
Abstract Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem (φ(x′))′=f(t,x,x′),x′(0)=0,x(1)=∫01x(s)dg(s), $$\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 : ℝn → ℝn is given by ϕ (s) = (φp1(s1), …, φpn(sn)), s ∈ ℝn, pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝn × ℝn → ℝn is continuous and g : [0,1] → ℝn is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.
Journal Title: Mathematica Slovaca
Year Published: 2018
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