On Some Spectral Properties of Third Order Nonlinear Boundary Value Problems

Abstract

<jats:p>The present paper deals with a two point the third-order nonlinear boundary value problem. An estimation of the number of solutions to boundary value problem and their nodal structure are established. Some results are given on spectral properties of solutions.</jats:p>

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

“…Moldojarov used the method of integral equations and the contraction mapping was used for proof unique solvability of nonlocal problem with integral conditions for a nonlinear PDE of the third order [140]. Smirnov investigated the third-order nonlinear BVP with twopoint NBC [209,210]. An estimation of the number of solutions to BVP and their nodal structure are established.…”

Nonlocal Third Order Boundary Value Problems With Solutions That Change Sign

“…Analogous technique was used by the author [10] to provide results on the estimation of the number of solutions to the boundary value problem for equation (1.1) subject to the two point conditions x(0) = x (0) = 0, x(1) = 0.…”

“…Also one example is given to illustrate the results. In order the paper to be self-contained, we provide some auxiliary results, published in [10] with proofs.…”

Properties of Zeros of Solutions to Third Order Nonlinear Differential Equations

“…The existence, location and properties of the zeros of the solutions of ordinary differential equations are of principal importance in the theory of boundary value problems [5,6,7], and correspondingly a vast literature on this subject has arisen. Among numerous papers dealing with this subject we refer the reader in particular to [2,3] for linear equations, and [1,4,8] for nonlinear equations.…”