EUDML

In this paper we develop the monotone method in the presence of upper and lower solutions for the $2$ nd order Lidstone boundary value problem $u^{(2 n)} (t) = f (t, u (t), u^{''} (t), \dots, u^{(2 (n - 1))} (t)), 0 < t < 1, u^{(2 i)} (0) = u^{(2 i)} (1) = 0, 0 \leq i \leq n - 1,$ where $f [0, 1] \times ℝ^{n} \to ℝ$ is continuous. We obtain sufficient conditions on $f$ to guarantee the existence of solutions between a lower solution and an upper solution for the higher order boundary value problem.

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The existence of countably many positive solutions for nonlinear $n$ th-order three-point boundary value problems.

Existence of solutions for $m$ -point boundary value problems on a half-line.

Existence of three positive solutions for $m$ -point discrete boundary value problems with $p$ -Laplacian.

Existence of triple positive solutions for second-order discrete boundary value problems.

Multiple positive solutions for singular quasilinear multipoint BVPs with the first-order derivative.

Existence of positive solutions for singular second order boundary value problems.

The method of upper and lower solutions for a Lidstone boundary value problem