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Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.