Existence of solutions to some singular initial value problems

Energy Analysis of Some Singular Initial Value Problems

This paper deals with a problem of conservation of energy in a singular initial value problem. These kind of problems appear in the study of radially symmetric elliptic and hyperbolic boundary value problems. The interesting question that arises is how to analyze the oscillation of the solutions, count the number of nodes and estimate their location. In order to conduct the analysis we need to ...

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 Solutions for Some Third-order Boundary-value Problems

In this paper concerns the third-order boundary-value problem u′′′(t) + f(t, u(t), u′(t), u′′(t)) = 0, 0 < t < 1, r1u(0)− r2u(0) = r3u(1) + r4u(1) = u′′(0) = 0. By placing certain restrictions on the nonlinear term f , we prove the existence of at least one solution to the boundary-value problem with the use of lower and upper solution method and of Schauder fixed-point theorem. The constructio...

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian

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.