scholarly journals The Existence of Symmetric Positive Solutions of Fourth-Order Elastic Beam Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 121 ◽  
Author(s):  
Münevver Tuz
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Point Theory ◽  
Beam Equations ◽  
Symmetric Positive Solutions ◽  
Elastic Beam Equations

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii.

scholarly journals Symmetric Positive Solutions for Nonlinear Singular Fourth-Order Eigenvalue Problems with Nonlocal Boundary Condition

2010 ◽  
Vol 2010 ◽  
pp. 1-16
Author(s):  
Fuyi Xu ◽  
Jian Liu
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Point Theory ◽  
Symmetric Positive Solution ◽  
Symmetric Positive Solutions

We investigate nonlinear singular fourth-order eigenvalue problems with nonlocal boundary conditionu(4)(t)-λh(t)f(t,u,u′′)=0,0<t<1,u(0)=u(1)=∫01a(s)u(s)ds,u′′(0)=u′′(1)=∫01b(s)u′′(s)ds, wherea,b∈L1[0,1],λ>0,hmay be singular att=0and/or1. Moreoverf(t,x,y)may also have singularity atx=0and/ory=0. By using fixed point theory in cones, an explicit interval forλis derived such that for anyλin this interval, the existence of at least one symmetric positive solution to the boundary value problem is guaranteed. Our results extend and improve many known results including singular and nonsingular cases. The associated Green's function for the above problem is also given.

scholarly journals Two positive solutions for nonlinear fourth-order elastic beam equations

2019 ◽  
pp. 1-12
Author(s):  
Giuseppina D'Aguì ◽  
Beatrice Di Bella ◽  
Patrick Winkert
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Elastic Beam ◽  
Beam Equations ◽  
Elastic Beam Equations

scholarly journals MULTIPLE POSITIVE SOLUTIONS OF BVPS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-CARATHEODORY NONLINEARITIES

2014 ◽  
Vol 19 (3) ◽  
pp. 395-416 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Elastic Beam ◽  
Multiple Positive Solutions ◽  
Beam Equations ◽  
Carathéodory Function ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Elastic Beam Equations

In this article, the existence of multiple positive solutions of boundary-value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x, x′ and x″, f may be singular at t = 0 and t = 1 and f is non-Caratheodory function. The analysis relies on the well known Schauder fixed point theorem and the five functional fixed point theorems in the cones.

scholarly journals Positive Solutions forp-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Value System ◽  
Existence Of Positive Solutions

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fourth-order differential equations with integral boundary conditions. By using the fixed point theory in cones, explicit range forλandμis derived such that for anyλandμlie in their respective interval, the existence of at least one positive solution to the boundary value system is guaranteed.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

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