On a class of $m$-point boundary value problems

Rodica Luca

Displaying similar documents to “On a class of $m$ -point boundary value problems”

Unbounded solutions of second-order multipoint boundary value problem on the half-line.

Liu, Lishan, Hao, Xinan, Wu, Yonghong (2010)

Boundary Value Problems [electronic only]

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Existence of positive solutions for nonlinear eigenvalue problems.

Wang, Sheng-Ping, Wong, Fu-Hsiang, Kung, Fan-Kai (2010)

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Existence of multiple positive solutions of $n th$ -order $m$ -point boundary value problems

Sihua Liang, Jihui Zhang (2010)

Mathematica Bohemica

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The paper deals with the existence of multiple positive solutions for the boundary value problem $\{\begin{matrix} {(ϕ (p (t) u^{(n - 1)}) (t))}^{'} + a (t) f (t, u (t), u^{'} (t), ..., u^{(n - 2)} (t)) = 0, 0 < t < 1, \\ u^{(i)} (0) = 0, i = 0, 1, ..., n - 3, \\ u^{(n - 2)} (0) = \sum_{i = 1}^{m - 2} α_{i} u^{(n - 2)} (ξ_{i}), u^{(n - 1)} (1) = 0, \end{matrix}$ where $ϕ : ℝ \to ℝ$ is an increasing homeomorphism and a positive homomorphism with $ϕ (0) = 0$ . Using a fixed-point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.