scholarly journals On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations

2004 ◽  
Vol 56 (6) ◽  
pp. 919-935 ◽  
Author(s):  
Yūki Naito ◽  
Satoshi Tanaka
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Second Order Differential Equations

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 Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations

2001 ◽  
Vol 162 ◽  
pp. 127-148 ◽  
Author(s):  
Zhongli Wei ◽  
Changci Pang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

This paper investigates the existence of positive solutions of nonresonant singular boundary value problem of second order differential equations. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.

The existence of multiple solutions for a Ginzburg–Landau type model of superconductivity

1996 ◽  
Vol 7 (6) ◽  
pp. 559-574 ◽  
Author(s):  
S. P. Hastings ◽  
M. K. Kwong ◽  
W. C. Troy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Type Model ◽  
Ginzburg Landau ◽  
Second Order Differential Equations ◽  
Parameter Values ◽  
Superconductor Material

We study a system of two second-order differential equations with cubic nonlinearities which model a film of superconductor material subjected to a tangential magnetic field. We verify some recent conjectures of one of the authors about multiplicity of solutions. We show that for an appropriate range of parameter values the relevant boundary value problem has at least two symmetric solutions. It is also proved that a second range of parameters exists for which there are three symmetric solutions.

scholarly journals Multiple solutions of boundary value problem

2006 ◽  
Vol 37 (2) ◽  
pp. 149-154
Author(s):  
Yongjin Li ◽  
Xiaobao Shu ◽  
Yuantong Xu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Group Index ◽  
Variational Structure

By means of variational structure and $ Z_2 $ group index theory, we obtain multiple solutions of boundary value problems for second-order ordinary differential equations$ \begin{cases} & - (ru')' + qu = \lambda f(t, u),\qquad 0 < t < 1 \\ & u'(0) = 0 = \gamma u(1)+ u'(1), \qquad \text{ where } \gamma \geq 0. \end{cases} $

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