Three positive solutions of fourth-order problems with clamped beam boundary conditions
Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
Cited by 2 publications
References 13 publications
In this article, we focus on the existence of positive solutions and establish a corresponding iterative scheme for a nonlinear fourth-order equation with indefinite weight and Neumann boundary conditions y ( 4 ) ( x ) + ( k 1 + k 2 ) y ″ ( x ) + k 1 k 2 y ( x ) = λ h ( x ) f ( y ( x ) ) , x ∈ [ 0 , 1 ] , y ′ ( 0 ) = y ′ ( 1 ) = y ‴ ( 0 ) = y ‴ ( 1 ) = 0 , \left\{\begin{array}{l}{y}^{\left(4)}\left(x)+\left({k}_{1}+{k}_{2}){y}^{^{\prime\prime} }\left(x)+{k}_{1}{k}_{2}y\left(x)=\lambda h\left(x)f(y\left(x)),\hspace{1em}x\in \left[0,1],\\ y^{\prime} \left(0)=y^{\prime} \left(1)={y}^{\prime\prime\prime }\left(0)={y}^{\prime\prime\prime }\left(1)=0,\\ \end{array}\right. where k 1 {k}_{1} and k 2 {k}_{2} are constants, λ > 0 \lambda \gt 0 is a parameter, h ( x ) ∈ L 1 ( 0 , 1 ) h\left(x)\in {L}^{1}\left(0,1) may change sign, and f ∈ C ( [ 0 , 1 ] × R + , R ) f\in C\left(\left[0,1]\times {{\mathbb{R}}}^{+},{\mathbb{R}}) , R + ≔ [ 0 , ∞ ) {{\mathbb{R}}}^{+}:= \left[0,\infty ) . We first discuss the sign properties of Green’s function for the elastic beam boundary value problem, and then we establish some new results of the existence of positive solutions to this problem if the nonlinearity f f is monotone on R + {{\mathbb{R}}}^{+} . The technique for dealing with this article relies on a monotone iteration technique and Schauder’s fixed point theorem. Finally, an example is presented to illustrate the application of our main results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
Contact Info
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Product
Resources
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.
