Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results

A class of nth-order BVPs with nonlocal conditions

AbstractThe aim of this paper is to present some existence results for a nonlinear nth-order boundary value problem with nonlocal conditions. Various fixed point theorems are used in the proofs. Examples are included to illustrate the results

Boundedness and convergence to zero of solutions of a forced second-order nonlinear differential equation

AbstractSufficient conditions for continuability, boundedness, and convergence to zero of solutions of (a(t)x′)′ + h(t, x, x′) + q(t) f(x) g(x′) = e(t, x, x′) are given

Existence of homoclinic solutions for second order difference equations with p-Laplacian

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation described in the paper

On the stability, boundedness, and square integrability of solutions of third order neutral delay differential equations

In this paper, sufficient conditions are established for the stability, boundedness and square integrability of solutions for some non-linear neutral delay differential equations of third order. Lyapunov’s direct method is used to obtain the results

Asymptotic Properties of Kneser Solutions to Third-Order Delay Differential Equations

The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established

Positive Solutions of a Nonlinear N-th Order Eigenvalue Problem

For 1/2 \u3c p \u3c 1 fixed, values of lambda \u3e 0 are determined for which there exist positive solutions of the n-th order differential equation u((n)) = lambda g(t)f(u), 0 \u3c t \u3c 1, satisfying the three-point boundary conditions, u((i-1)) (0) = u((n-2)) (P) = u((n-1)) (1) = 0, 1 The problem is converted to a third order differential-integro boundary value problem and then a recent result of Graef and Yang for third order boundary value problems is adapted. An example is included to illustrate the results

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory