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POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Asif, Naseer Ahmad,Eloe, Paul W.,Khan, Rahmat Ali Korean Mathematical Society 2010 대한수학회지 Vol.47 No.5
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type -x"(t) = f(t, y(t)), t $\in$ (0, 1), -y"(t) = g(t, x(t)), t $\in$ (0, 1), x(0) = y(0) = 0, x(1) = ${\alpha}x(\eta)$, y(1) = ${\alpha}y(\eta)$, are obtained. The nonlinearities f, g : (0,1) $\times$ (0, $\infty$ ) $\rightarrow$ (0, $\infty$) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters $\eta$, $\alpha$, satisfy ${\eta}\;{\in}\;$ (0,1), 0 < $\alpha$ < $1/{\eta}$. An example is provided to illustrate the results.
POSITIVE SOLUTIONS FOR A SYSTEM OF SINGULAR SECOND ORDER NONLOCAL BOUNDARY VALUE PROBLEMS
Naseer Ahmad Asif,Paul W. Eloe,Rahmat Ali Khan 대한수학회 2010 대한수학회지 Vol.47 No.5
Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type [수식],[수식],[수식]are obtained. The nonlinearities f, g : (0, 1) × (0,1)→ (0,∞) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. The parameters η,α satisfy η ∈ (0, 1), 0 < α < 1/η. An example is provided to illustrate the results.