scholarly journals Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Integral Type ◽  
One Dimensional ◽  
Second Order Differential Equations ◽  
Type Boundary ◽  
The One

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensionalp-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensionalp-Laplacian term[ρ(t)Φ(x’(t))]’involved with the functionρ, which makes the solutions un-concave.

scholarly journals The existence of three positive solutions to integral type BVPs for singular second ODEs with one-dimensional p-Laplacian

2011 ◽  
Vol 27 (2) ◽  
pp. 239-248
Author(s):  
YUJI LIU ◽  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Singular Differential Equations ◽  
One Dimensional ◽  
Type Boundary ◽  
The One

This paper is concerned with the integral type boundary value problems of the second order singular differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three positive solutions are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x 0 (t))]0 involved with the function ρ, which makes the solutions un-concave. Furthermore, f, g, h and ρ may be singular at t = 0 or t = 1.

Geometric characterization of separable second-order differential equations

1993 ◽  
Vol 113 (1) ◽  
pp. 205-224 ◽  
Author(s):  
Eduardo Martínez ◽  
José F. Cariñena ◽  
Willy Sarlet
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Geometric Characterization ◽  
One Dimensional ◽  
Practical Procedure ◽  
Second Order Differential Equations ◽  
Necessary And Sufficient ◽  
Second Order Equations

AbstractWe establish necessary and sufficient conditions for the separability of a system of second-order differential equations into independent one-dimensional second-order equations. The characterization of this property is given in terms of geometrical objects which are directly related to the system and relatively easy to compute. The proof of the main theorem is constructive and thus yields a practical procedure for constructing coordinates in which the system decouples.

scholarly journals SOLVABILITY OF BOUNDARY VALUE PROBLEMS FOR SINGULAR QUASI-LAPLACIAN DIFFERENTIAL EQUATIONS ON THE WHOLE LINE

2012 ◽  
Vol 17 (3) ◽  
pp. 423-446 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Continuous Operator ◽  
Completely Continuous ◽  
One Dimensional ◽  
Type Boundary ◽  
The One

This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the one-dimensional p-Laplacian term involving a nonnegative function ρ that may be singular at t = 0 and such that . A Banach space and a nonlinear completely continuous operator are defined in this paper. By using the Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established. An example is presented to illustrate the main theorem.

Positive Solutions to Second Order Singular Differential Equations Involving the One-Dimensional M-Laplace Operator

1999 ◽  
Vol 6 (4) ◽  
pp. 347-362
Author(s):  
Tomoyuki Tanigawa
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Second Order ◽  
Singular Differential Equations ◽  
One Dimensional ◽  
The One ◽  
Positive Half

Abstract We consider a class of second order quasilinear differential equations with singular ninlinearities. Our main purpose is to investigate in detail the asymptotic behavior of their solutions defined on a positive half-line. The set of all possible positive solutions is classified into five types according to their asymptotic behavior near infinity, and sharp conditions are established for the existence of solutions belonging to each of the classified types.

scholarly journals New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1159
Author(s):  
Shyam Sundar Santra ◽  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Fluid Dynamics ◽  
Neural Networks ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals Boundedness of Solutions for Second Order Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 58
Author(s):  
Daniel C. Biles
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Boundedness Of Solutions ◽  
Second Order Differential Equations ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

We present new theorems which specify sufficient conditions for the boundedness of all solutions for second order non-linear differential equations. Unboundedness of solutions is also considered.

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