Positive solutions to a second order three-point boundary value problem

Positive solutions to a generalized second order three-point boundary value problem

Let T be a time scale with 0, T ∈ T. We investigate the existence and multiplicity of positive solutions to the nonlinear second-order three-point boundary-value problem u∆∇(t) + a(t)f(u(t)) = 0, t ∈ [0, T ] ⊂ T, u(0) = βu(η), u(T ) = αu(η) on time scales T, where 0 < η < T , 0 < α < T η , 0 < β < T−αη T−η are given constants.

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Positive Solutions to a Singular Second Order Boundary Value Problem

In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...

Positive Solutions to a Second-Order Discrete Boundary Value Problem

Positive Solutions for a Functional Delay Second-order Three-point Boundary-value Problem

We establish criteria for the existence of positive solutions to the three-point boundary-value problems expressed by second-order functional delay differential equations of the form −x′′(t) = f(t, x(t), x(t− τ), xt), 0 < t < 1, x0 = φ, x(1) = x(η), where φ ∈ C[−τ, 0], 0 < τ < 1/4, and τ < η < 1.