Asymptotic behavior of solutions of fourth-order linear ordinary differential equations

1977 ◽  
Vol 29 (1) ◽  
pp. 82-87
Author(s):  
E. S. Kostenko
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Asymptotic Behavior Of Solutions ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

scholarly journals The distribution of nonprincipal eigenvalues of singular second-order linear ordinary differential equations

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Pablo Pinasco
Keyword(s):  
Asymptotic Behavior ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Asymptotic Distribution ◽  
Counting Function ◽  
Infinite Interval ◽  
Singular Problem ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problemx″+λq(t)x=0on an infinite interval[a,+∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl-type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.

Asymptotic behavior of the curves in the Fučík spectrum

2016 ◽  
Vol 19 (04) ◽  
pp. 1650039 ◽  
Author(s):  
Juan Pablo Pinasco ◽  
Ariel Martin Salort
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hyperbolic Type ◽  
Type Curves ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Fučík Spectrum ◽  
Fučik Spectrum ◽  
Fucik Spectrum

In this work, we study the asymptotic behavior of the curves of the Fučík spectrum for weighted second-order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fučík spectrum with rays through the origin, and we compare their values with the asymptotic ones.

scholarly journals Two non-elementary integral functions defined using central factorial powers

2015 ◽  
Vol 23 ◽  
pp. 98
Author(s):  
T.P. Goy
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Variable Coefficients ◽  
Elementary Functions ◽  
Order Linear ◽  
Linear Ordinary Differential Equations

We study two new real-valued non-elementary functions generated by central factorial powers. Graphs of such functions are plotted and some of their properties are proved. It is also shown that new integral functions are solutions of fourth order linear ordinary differential equations with variable coefficients.

Remark on zeros of solutions of second-order linear ordinary differential equations

2016 ◽  
Vol 23 (4) ◽  
pp. 571-577
Author(s):  
Monika Dosoudilová ◽  
Alexander Lomtatidze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Nontrivial Solution ◽  
Unique Solvability ◽  
Periodic Boundary ◽  
Periodic Boundary Value Problem ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Zeros Of Solutions

AbstractAn efficient condition is established ensuring that on any interval of length ω, any nontrivial solution of the equation ${u^{\prime\prime}=p(t)u}$ has at most one zero. Based on this result, the unique solvability of a periodic boundary value problem is studied.

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