Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-06
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
In this paper, we consider the existence of positive solutions for the fully fourth-order boundary value problem u4t=ft,ut,u′t,u″t,u‴t, 0≤t≤1,u0=u1=u″0=u″1=0, where f:0,1×0,+∞×−∞,+∞×−∞,0×−∞,+∞⟶0,+∞ is continuous.
This equation can simulate the deformation of an elastic beam simply supported at both ends in a balanced state.
By using the fixed-point index theory and the cone theory, we discuss the existence of positive solutions of the fully fourth-order boundary value problem.
We transform the fourth-order differential equation into a second-order differential equation by order reduction method.
And then, we examine the spectral radius of linear operators and the equivalent norm on continuous space.
After that, we obtain the existence of positive solutions of such BVP.
American Psychological Association (APA)
Zhang, Yixin& Cui, Yujun. 2020. Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1201574
Modern Language Association (MLA)
Zhang, Yixin& Cui, Yujun. Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms. Mathematical Problems in Engineering No. 2020 (2020), pp.1-7.
https://search.emarefa.net/detail/BIM-1201574
American Medical Association (AMA)
Zhang, Yixin& Cui, Yujun. Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1201574
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1201574