scholarly journals Nodal solutions for a second-order m-point boundary value problem

2006 ◽  
Vol 56 (4) ◽  
pp. 1243-1263 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Nodal Solutions

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.

scholarly journals Solvability of singular second order m-point boundary value problems of Dirichlet type

2005 ◽  
Vol 71 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Ruyun Ma ◽  
Bevan Thompson
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Continuation Theorem ◽  
Point Boundary ◽  
Dirichlet Type ◽  
Carathéodory Conditions

Let f: [0, 1] × ℝ2 → ℝ be a function satisfying the Carathéodory conditions and t (1 − t) e (t) ∈ L1(0, 1). Let ai ∈ ℝ and ξi ∈ (0, 1) for i = 1, …, m − 2 where 0 < ξ1 < ξ2 < … < ξm−2 < 1. In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem The proof of our main result is based on the Leray-Schauder continuation theorem.

scholarly journals On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Yuri E. Gliklikh ◽  
Peter S. Zykov
Keyword(s):  
Boundary Value Problem ◽  
Riemannian Manifolds ◽  
Boundary Value ◽  
Second Order ◽  
Quadratic Growth ◽  
Point Boundary ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Differential Equations And Inclusions ◽  
Complete Riemannian Manifolds

The two-point boundary value problem for second-order differential inclusions of the form(D/dt)m˙(t)∈F(t,m(t),m˙(t))on complete Riemannian manifolds is investigated for a couple of points, nonconjugate along at least one geodesic of Levi-Civitá connection, whereD/dtis the covariant derivative of Levi-Civitá connection andF(t,m,X)is a set-valued vector with quadratic or less than quadratic growth in the third argument. Some interrelations between certain geometric characteristics, the distance between points, and the norm of right-hand side are found that guarantee solvability of the above problem forFwith quadratic growth inX. It is shown that this interrelation holds for all inclusions withFhaving less than quadratic growth inX, and so for them the problem is solvable.

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