Existence of solutions to derivative-dependent, nonlinear singular boundary value problems

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Existence of Three Positive Solutions to Nonlinear Boundary Value Problems

Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations

In this paper, we consider the properties of the Green’s function for the nonlinear fractional differential equation boundary value problem Dq0+u(t) = f (t,u(t)), t ∈ J := [0, 1], u(0) = u′(1) = 0, where 1 < q≤ 2 is a real number, and Dq0+ is the standard Riemann-Liouville differentiation. As an application of the Green’s function, we give some multiple positive solutions for singular boundary ...

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...