Asymptotic Behavior of Slowly Varying Solutions of Second-Order Ordinary Binomial Differential Equations with Rapidly Varying Nonlinearity
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DOI: 10.1007/s10958-018-4111-7
Abstract: We establish new conditions for the existence of slowly varying solutions of a second-order differential binomial nonautonomous equation with rapidly varying nonlinearity. We also determine the asymptotic representations for these solutions and their first derivatives… read more here.
Keywords: slowly varying; solutions second; second order; varying nonlinearity ... See more keywords
Asymptotics of the Solutions of Second-Order Differential Equations with Regularly and Rapidly Varying Nonlinearities
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DOI: 10.1007/s10958-019-04546-w
Abstract: We establish conditions for the existence of a class of monotone solutions of the second-order differential equations with regularly and rapidly varying nonlinearities and the asymptotic representations of these solutions as t ↑ ω (ω… read more here.
Keywords: solutions second; equations regularly; second order; regularly rapidly ... See more keywords
Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation
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DOI: 10.1155/2020/4871812
Abstract: In this work, we assume that the readers are familiar with general definitions and fundamental theories of Nevanlinna theory [1–3]. f is a meromorphic function which means f is meromorphic in the finite complex plane… read more here.
Keywords: difference; solutions second; second order; order fermat ... See more keywords
Existence of Oscillatory Solutions for Second‐Order Functional Differential Equations With Time Delay
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DOI: 10.1155/jofs/6689726
Abstract: This paper investigates the existence of oscillatory behavior of solutions for the following second‐order delay differential equation By using the Schauder–Tychonoff fixed‐point theorem and Ascoli–Arzelà theorem, sufficient conditions for the existence of oscillatory solutions are… read more here.
Keywords: solutions second; existence oscillatory; delay; oscillatory solutions ... See more keywords
On the method of finding periodic solutions of second-order neutral differential equations with piecewise constant arguments
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DOI: 10.1186/s13662-017-1396-7
Abstract: This paper provides a method of finding periodical solutions of the second-order neutral delay differential equations with piecewise constant arguments of the form x″(t)+px″(t−1)=qx(2[t+12])+f(t)$x''(t)+px''(t-1)=qx(2[\frac{t+1}{2}])+f(t)$, where [⋅]$[\cdot]$ denotes the greatest integer function, p and q are… read more here.
Keywords: order neutral; solutions second; second order; method finding ... See more keywords
On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations
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DOI: 10.1515/gmj-2017-0009
Abstract: Abstract Sufficient conditions for the existence of periodic, bounded, and unbounded solutions of the equation u ′′ = f ( t , u ) {u^{\prime\prime}=f(t,u)} are proved. read more here.
Keywords: solutions second; unbounded solutions; bounded unbounded; second order ... See more keywords
Infinite growth of solutions of second order complex differential equation
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DOI: 10.1515/math-2018-0103
Abstract: Abstract In this paper we study the growth of solutions of second order differential equation f′′ + A(z)f′ + B(z)f = 0. Under certain hypotheses, the non-trivial solution of this equation is of infinite order. read more here.
Keywords: growth solutions; order; solutions second; differential equation ... See more keywords
On the Oscillatory Behavior of Solutions of Second-Order Non-Linear Differential Equations with Damping Term
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DOI: 10.3390/math12071096
Abstract: In this paper, we discuss the oscillatory behavior of solutions of two general classes of nonlinear second-order differential equations. New criteria are obtained using Riccati transformations and the integral averaging techniques. The obtained results improve… read more here.
Keywords: behavior solutions; oscillatory behavior; differential equations; solutions second ... See more keywords
Asymptotic behavior of solutions of second-order difference equations of Volterra type
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DOI: 10.3906/mat-1904-30
Abstract: We establish sufficient conditions for the existence of a solution x of the above equation with the property xn = yn+o(n), where y is a given solution of the equation ∆(rn∆yn) = bn and s… read more here.
Keywords: asymptotic behavior; difference equations; solutions second; second order ... See more keywords
Some multiplicity results of homoclinic solutions for second order Hamiltonian systems
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DOI: 10.7494/opmath.2020.40.1.21
Abstract: where q : R → R , W ∈ C1(R × R ,R) and ∇W (t, q) denotes the gradient of W with respect to q ∈ R for every t ∈ R. We look… read more here.
Keywords: solutions second; results homoclinic; second order; homoclinic solutions ... See more keywords