Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

We study the existence of multiple nonnegative solutions for the doubly singular threepoint boundary value problem with derivative dependent data function − p t y′ t ′ q t f t, y t , p t y′ t , 0 < t < 1, y 0 0, y 1 α1y η . Here, p ∈ C 0, 1 ∩ C1 0, 1 with p t > 0 on 0, 1 and q t is allowed to be discontinuous at t 0. The fixed point theory in a cone is applied to achieve new and more general re...

Nontrivial Solutions for Singular Nonlinear Three-Point Boundary Value Problems

The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...

Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

Multiple Positive Solutions for Singular Boundary-value Problems with Derivative Dependence on Finite and Infinite Intervals

In this paper, Krasnoselskii’s theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.

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...