scholarly journals ON ASYMPTOTIC CLASSIFICATION OF SOLUTIONS TO FOURTH-ORDER DIFFERENTIAL EQUATIONS WITH SINGULAR POWER NONLINEARITY

2016 ◽  
Vol 21 (4) ◽  
pp. 502-521 ◽  
Author(s):  
Irina Astashova
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Fourth Order ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
All Solutions ◽  
Classification Of Solutions ◽  
Type Differential Equation

The asymptotic behavior of all solutions to the fourth-order Emden– Fowler type differential equation with singular nonlinearity is investigated. The equation is transformed into a system on the three-dimensional sphere. By investigation of the asymptotic behavior of all possible trajectories of this system an asymptotic classification of all solutions to the equation is obtained.

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

The limit-4 case of fourth-order self-adjoint differential equations

1977 ◽  
Vol 79 (1-2) ◽  
pp. 51-59 ◽  
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fourth Order ◽  
Asymptotic Theory ◽  
Order Differential Equation ◽  
New Method ◽  
All Solutions ◽  
Image Position ◽  
Fourth Order Differential Equation

SynopsisA new method is developed for identifying real-valued coefficientsr(x),p(x), andq(x)for which all solutions of the fourth-order differential equationareL2(0, ∞). The results are compared with those derived from the asymptotic theory of Devinatz, Walker, Kogan and Rofe-Beketov.

scholarly journals Unbounded solutions for differential equations with p-Laplacian and mixed nonlinearities

2017 ◽  
Vol 24 (1) ◽  
pp. 15-28
Author(s):  
Miroslav Bartušek ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Second Order ◽  
Unbounded Solutions ◽  
Order Nonlinear Differential Equation ◽  
All Solutions ◽  
Mixed Nonlinearities

AbstractThe existence of unbounded solutions with different asymptotic behavior for a second order nonlinear differential equation withp-Laplacian is considered. The oscillation of all solutions is investigated. Some discrepancies and similarities between equations of Emden–Fowler-type and equations with mixed nonlinearities are pointed out.

scholarly journals Simplified and improved criteria for oscillation of delay differential equations of fourth order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Moaaz ◽  
A. Muhib ◽  
D. Baleanu ◽  
W. Alharbi ◽  
E. E. Mahmoud
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Point ◽  
All Solutions ◽  
Special Cases ◽  
Delay Differential ◽  
Noncanonical Operator

AbstractAn interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

scholarly journals Comparison theorems for fourth order differential equations

1986 ◽  
Vol 9 (1) ◽  
pp. 105-109
Author(s):  
Garret J. Etgen ◽  
Willie E. Taylor
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Linear Equations ◽  
Oscillation Criterion ◽  
Comparison Theorems ◽  
Positive Continuous Function ◽  
Order Linear ◽  
All Solutions

This paper establishes an apparently overlooked relationship between the pair of fourth order linear equationsyiv−p(x)y=0andyiv+p(x)y=0, wherepis a positive, continuous function defined on[0,∞). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.

scholarly journals Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Cemil Tunç ◽  
Muzaffer Ateş
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Cauchy Formula ◽  
Boundedness Of Solutions ◽  
Constant Coefficients ◽  
Particular Solution

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.

Additional spectral properties of the fourth-order Bessel-type differential equation

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1538-1549 ◽  
Author(s):  
W. N. Everitt ◽  
H. Kalf ◽  
L. L. Littlejohn ◽  
C. Markett
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Spectral Properties ◽  
Type Differential Equation
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