Abstract
Multiple positive solutions for nonlinear third order general two-point boundary value problems
Highlights
In this paper we consider the existence of positive solutions to the third order nonlinear differential equation, y (t) + f (t, y(t)) = 0, t ∈ [a, b], (1)
There is much current attention focussed on existence of positive solutions to the boundary value problems for ordinary differential equations, as well as for the finite difference equations; see [5, 6, 8, 9] to name a few
In [23], Sun and Wen considered the existence of multiple positive solutions to third order equation, y (t) = a(t)f (y(t)), 0 < t < 1 under the boundary conditions αy (0) − βy (0) = 0, y(1) = y (1) = 0
Summary
In this paper we consider the existence of positive solutions to the third order nonlinear differential equation, y (t) + f (t, y(t)) = 0, t ∈ [a, b],. Shuhong and Li [22] obtained the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem y (t)+λa(t)f (y(t)) = 0, 0 < t < 1 y(0) =y (0) = y (1) = 0 by using Krasnosel’skii fixed point theorem [16]. In [23], Sun and Wen considered the existence of multiple positive solutions to third order equation, y (t) = a(t)f (y(t)), 0 < t < 1 under the boundary conditions αy (0) − βy (0) = 0, y(1) = y (1) = 0. We give two examples to demonstrate our results
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