On boundary-value problems for partial differential equations of order higher than two

Jan Popiołek

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A boundary value problem for non-linear differential equations with a retarded argument

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Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities

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We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.