scholarly journals Homoclinic solutions for linear and linearizable ordinary differential equations

2000 ◽  
Vol 5 (2) ◽  
pp. 65-83 ◽  
Author(s):  
Cezar Avramescu ◽  
Cristian Vladimirescu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value ◽  
Existence Results ◽  
Homoclinic Solutions ◽  
Infinite Boundary Value Problem

Using functional arguments, some existence results for the infinite boundary value problemx˙=F(t,x),x(−∞)=x(+∞)are given. A solution of this problem is frequently called, from Poincaré, homoclinic.

Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations

1988 ◽  
Vol 31 (1) ◽  
pp. 79-84
Author(s):  
P. W. Eloe ◽  
P. L. Saintignon
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Linear Differential Operator ◽  
Boundary Value ◽  
Linear Differential ◽  
Type Boundary ◽  
Sign Conditions ◽  
Conjugate Type

AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

Existence theorems for equations in normed spaces and boundary value problems for nonlinear vector ordinary differential equations

1984 ◽  
Vol 98 (1-2) ◽  
pp. 1-11 ◽  
Author(s):  
A. Cañada ◽  
R. Ortega
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Linear Part ◽  
Sufficient Conditions ◽  
First Eigenvalue ◽  
Normed Spaces ◽  
Nonlinear Vector

SynopsisThe existence of solutions to equations in normed spaces is proved when the nonlinear part of the equation satisfies growth and asymptotic conditions, whether the linear part is invertible or not. For this, we use the coincidence degree theory developed by Mawhin. We apply our abstract results to boundary value problems for nonlinear vector ordinary differential equations. In particular, we consider the Picard boundary value problem at the first eigenvalue and the periodic boundary value problem at resonance. In both cases, the nonlinear term can be of superlinear type. Also, necessary and sufficient conditions of Landesman-Lazer type are obtained.

Positive and maximal positive solutions of singular mixed boundary value problem

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Ravi Agarwal ◽  
Donal O’Regan ◽  
Svatoslav Staněk
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Mixed Boundary Value Problem ◽  
Time Singularity ◽  
Strong Singularity

AbstractThe paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.

Boundary value problems on noncompact intervals

1995 ◽  
Vol 125 (4) ◽  
pp. 777-799 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Existence Results ◽  
Second Order

Existence results are established for second-order boundary value problems for ordinary differential equations on non-compact intervals.

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