ANALYSIS OF POSITIVE SOLUTIONS FOR A FOURTH-ORDER BEAM EQUATION WITH SIGN-CHANGING GREEN’S FUNCTION

Huijuan Zhu; Fanglei Wang

doi:10.1216/jie.2024.36.493

Abstract

We investigate the existence of positive solutions for a fourth-order beam equation

$\{ \matrix{{u^{(4)} (x) - \lambda u^{\prime \prime } (x) = \mu h(x)f(u(x)),} \hfill & {x \in [0,1],} \hfill \cr {u(0) = u^{\prime \prime } (0) = u(1) = 0,} \hfill & {} \hfill \cr {\delta u^{\prime \prime } (1) - u^{\prime \prime \prime } (\zeta ) + \lambda u^\prime (\zeta ) = 0} \hfill & {} \hfill \cr }$

with sign-changing Green’s function. Combine a priori estimates of Green’s function, we apply the Leray–Schauder fixed point theorem to obtain the existence of positive solutions. We give the Ulam–Hyers stability result of the solution for the equation.

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Huijuan Zhu. Fanglei Wang. "ANALYSIS OF POSITIVE SOLUTIONS FOR A FOURTH-ORDER BEAM EQUATION WITH SIGN-CHANGING GREEN’S FUNCTION." J. Integral Equations Applications 36 (4) 493 - 514, Winter 2024. https://doi.org/10.1216/jie.2024.36.493

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Received: 1 April 2024; Revised: 10 June 2024; Accepted: 1 July 2024; Published: Winter 2024

First available in Project Euclid: 3 October 2024

Digital Object Identifier: 10.1216/jie.2024.36.493

Subjects:

Primary: 34B18 , 34B27

Keywords: Beam equation , fixed point Theorem , ‎positive‎ ‎solutions , sign-changing Green’s function

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