Oscillation of second-order hyperbolic equations with non-integrable coefficients

1982 ◽  
Vol 91 (3-4) ◽  
pp. 305-313 ◽  
Author(s):  
Wu-Teh Hsiang ◽  
Man Kam Kwong
Keyword(s):  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Case ◽  
Linear Hyperbolic Equation ◽  
Initial Values ◽  
Non Linear ◽  
Image Position

SynopsisSome sufficient conditions are obtained on the coefficient g and the initial values Φ and ψfor the solution ot the non-linear hyperbolic equationto change sign in the first quadrant. An example is given to show that is not sufficient in the linear case.

scholarly journals The Cauchy problem for a second-order nonlinear hyperbolic equation with initial data on a line of parabolicity

1979 ◽  
Vol 20 (3) ◽  
pp. 345-365
Author(s):  
John M.S. Rassias
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equation ◽  
Initial Conditions ◽  
Small Neighborhood ◽  
Second Order ◽  
Nonlinear Hyperbolic Equation ◽  
Linear Hyperbolic Equation ◽  
The Cauchy Problem ◽  
Upper Half Plane ◽  
Image Position

In this paper we study the Cauchy problem for the second order nonlinear hyperbolic partial differential equationwith initial conditionswhereand |u|, |ux|, |uy| < ∞, y ≥ 0, r = r(x) ∈ C4(·), ν = ν(x) ∈ C4(·).These conditions on k, H, f, r, and ν are assumed to be satisfied in some sufficiently small neighborhood of the segment I, y = 0, in the upper half-plane y > 0This paper generalizes the results obtained by N.A. Lar'kin (Differencial'nye Uravnenija 8 (1972), 76–84), who has treated the special case H = H(x, y, u); that is, the quasi-linear hyperbolic equation (*).

On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order

2008 ◽  
Vol 15 (3) ◽  
pp. 555-569
Author(s):  
Tariel Kiguradze
Keyword(s):  
Hyperbolic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Hyperbolic Equation ◽  
Well Posedness ◽  
Nonlinear Hyperbolic Equations ◽  
Right Hand

Abstract In the rectangle Ω = [0, a] × [0, b] the nonlinear hyperbolic equation 𝑢(2,2) = 𝑓(𝑥, 𝑦, 𝑢) with the continuous right-hand side 𝑓 : Ω × ℝ → ℝ is considered. Unimprovable in a sense sufficient conditions of solvability of Dirichlet, Dirichlet–Nicoletti and Nicoletti boundary value problems are established.

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.

Nonlocal and Initial Problems for Quasilinear, Nonstrictly Hyperbolic Equations with General Solutions Represented by Superposition of Arbitrary Functions

2003 ◽  
Vol 10 (4) ◽  
pp. 687-707
Author(s):  
J. Gvazava
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Quasilinear Equations ◽  
General Solutions ◽  
Parabolic Degeneracy

Abstract We have selected a class of hyperbolic quasilinear equations of second order, admitting parabolic degeneracy by the following criterion: they have a general solution represented by superposition of two arbitrary functions. For equations of this class we consider the initial Cauchy problem and nonlocal characteristic problems for which sufficient conditions are established for the solution solvability and uniquness; the domains of solution definition are described.

scholarly journals On the Asymptotic Behavior of a Class of Second-Order Non-Linear Neutral Differential Equations with Multiple Delays

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 134 ◽  
Author(s):  
Shyam Sundar Santra ◽  
Ioannis Dassios ◽  
Tanusri Ghosh
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Theory ◽  
Second Order ◽  
Multiple Delays ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Non Linear ◽  
Delay Differential

In this work, we present some new sufficient conditions for the oscillation of a class of second-order neutral delay differential equation. Our oscillation results, complement, simplify and improve recent results on oscillation theory of this type of non-linear neutral differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

Oscillations of Second Order Neutral Differential Equations

1993 ◽  
Vol 36 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Shigui Ruan
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwhere t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.

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