Existence of solutions for a class of third-order nonlinear boundary value problem

2015

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DOI 10.1063/1.4936723
Data confidence 70 medium
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Abstract

Using a global existence result due to A. Granas et al. [7] and the barrier strips technique, we study the solvability of the boundary value problem x′′′ = f (t, x, x′, x′′), x(0) = A, x′(0) = B, x′′(1) = C where f :[0,1]×ℝ3→ℝ is continuous. The obtained sufficient conditions guarantee the existence of at least one solution in C3 [0,1] which may be nonnegative, monotone and convex.