scholarly journals Vibration of an axially loaded heterogeneous pinned-pinned beam with an intermediate roller support

2021 ◽  
Vol 16 (2) ◽  
pp. 99-128
Author(s):  
László Kiss ◽  
György Szeidl ◽  
Messaudi Abderrazek
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Solution Algorithm ◽  
Point Boundary ◽  
Effective Solution ◽  
Intermediate Roller ◽  
Roller Support ◽  
Algebraic Eigenvalue Problem

The present paper is devoted to the issue of what effect the axial load (compressive or tensile) has on the eigenfrequencies of a heterogeneous pinned-pinned beam with an intermediate roller support (called a PrsP beam). This problem is a three point boundary value problem (eigenvalue problem) associated with homogeneous boundary conditions. If the Green functions of the three point boundary value problem (BVP) are known the eigenvalue problem that provide the eigenfrequencies for the beam loaded axially can be transformed into an eigenvalue problem governed by a homogeneous Fredholm integral equation. The later eigenvalue problems can be reduced to an algebraic eigenvalue problem which then can be solved numerically by using an effective solution algorithm which is based on the boundary element method.

scholarly journals Some New Existence Results of Positive Solutions to an Even-Order Boundary Value Problem on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yanbin Sang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Point Boundary ◽  
Even Order

We consider a high-order three-point boundary value problem. Firstly, some new existence results of at least one positive solution for a noneigenvalue problem and an eigenvalue problem are established. Our approach is based on the application of three different fixed point theorems, which have extended and improved the famous Guo-Krasnosel’skii fixed point theorem at different aspects. Secondly, some examples are included to illustrate our results.

scholarly journals Existence Theorems for Some Classes of Boundary Value Problems Involving the P(X)-Laplacian

2008 ◽  
Vol 13 (2) ◽  
pp. 145-158
Author(s):  
Ionica Andrei
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Theoretical Approach ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problem ◽  
Existence Theorems ◽  
Boundary Value ◽  
Mountain Pass ◽  
Mountain Pass Lemma

We prove an alternative for a nonlinear eigenvalue problem involving the p(x)-Laplacian and study a subcritical boundary value problem for the same operator. The theoretical approach is the Mountain Pass Lemma and one of its variants, which is very useful in the study of eigenvalue problems.

scholarly journals Solvability of a nonlinear general third order four point eigenvalue problem on time scales

2011 ◽  
Vol 20 (2) ◽  
pp. 171-182
Author(s):  
S. NAGESWARA RAO ◽  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Four

We consider the four point boundary value problem for third order nonlinear differential equation on time scales ... subject to the boundary conditions ... t1 ≤ t2 ≤ t3 ≤ σ 3 (t4), α > 0, β > 0. Values of the parameter λ are determined for which the boundary value problem has a positive solution by utilizing a fixed point theorem on cone.

scholarly journals Perturbations near resonance for thep-Laplacian inℝN

2002 ◽  
Vol 7 (6) ◽  
pp. 323-334 ◽  
Author(s):  
To Fu Ma ◽  
Maurício Luciano Pelicer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Principal Eigenvalue ◽  
Multiplicity Result ◽  
Point Boundary ◽  
Three Solutions ◽  
Laplacian Equation ◽  
Near Resonance

We study a multiplicity result for the perturbedp-Laplacian equation−Δpu−λg(x)|u|p−2u=f(x,u)+h(x) in ℝN, where1<p<Nandλis nearλ 1, the principal eigenvalue of the weighted eigenvalue problem−Δpu=λg(x)|u|p−2uinℝN. Depending on which sideλis fromλ 1, we prove the existence of one or three solutions. This kind of result was firstly obtained by Mawhin and Schmitt (1990) for a semilinear two-point boundary value problem.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

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