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Monotone positive solutions of fourth-order boundary value problems with integral boundary conditions. (Chinese. English summary) Zbl 1449.34074

Summary: By using the monotone iterative technique, this article studies the existence of monotone positive solutions for fourth order boundary value problems with integral boundary conditions \[\begin{cases} u^{ (4)} (t) = f (t,u (t), u' (t)),\; t \in (0,1),\\ u (0) = u' (1) = u''' (1) = 0,\\ u'' (0) = \int_0^1 g (t)u'' (t){\mathrm{d}}t, \end{cases}\] where \(f:[0,1] \times [0,+\infty)^2 \to [0,+\infty)\) is continuous.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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