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Oscillation criteria of the Popov type
IEEE Transactions on Automatic Control, 1975Criteria of the Popov type are established for the existence of periodic motion in state space for a class of time invariant, autonomous, nonlinear feedback systems. In a restricted sense they constitute an extension of a previously obtained result [1].
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Oscillation Criteria for a 2-D Discrete System
Qualitative Theory of Dynamical Systems, 2016This paper is concerned with the oscillatory behavior of the \(2\)-D discrete system \[ u_{m-1,n} + u_{m,n-1} - p u_{m,n} + q u_{m+k,n+l} = 0, \tag{1} \] where \(p, q\) are real numbers and \(m, n, k, l\) are nonnegative integers. The investigation of the problem above is divided into four mutually exclusive cases: (i) \(k \geq 1\) and \(l\geq 1\), (ii)
Yuan, Chunhua, Zhang, Liang
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Oscillation criteria for difference equations with damping terms
Applied Mathematics and Computation, 2004The authors study the oscillation of second order nonlinear difference equations with damping of the form \[ \Delta(a_n(\Delta x_n)^\gamma)+p_n(\Delta x_n)^\gamma+q_nf(x_{n+1})=0, n=n_0,n_0+1, \cdots. \tag{1} \] By means of generalized Riccati transformation techniques, several new oscillation criteria are established for oscillation of all solutions ...
Samir H. Saker, Sui Sun Cheng
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Oscillation Criteria for a Class of Perturbed Schrödinger Equations
Canadian Mathematical Bulletin, 1982We are concerned with the oscillatory behavior of the second order elliptic equation1where Δ is the Laplace operator inn-dimensional Euclidean spaceRn,Eis an exterior domain inRn, andc:E × R → Randf:E → Rare continuous functions.A functionv : E − Ris called oscillatory inEifv(x) has arbitrarily large zeros, that is, the set {x∈E:v(x) = 0} is unbounded.
Kusano, Takasi, Naito, Manabu
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Oscillation Criteria for Third Order Differential Equations
SIAM Journal on Mathematical Analysis, 1976This paper gives some sufficient conditions for \[ y''' + p(x)y' + q(x)y = 0\] to have oscillatory solutions.
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Oscillation criteria for second order difference equation
Funkcialaj Ekvacioj, 1991Consider the difference equation \(\Delta^ 2x_{k-1}+b_ kx_ k=0\), \(k\geq 1\), where \(\Delta x_ k=x_{k+1}-x_ k\) and \(b_ k\geq 0\) with infinitely many positive terms. This equation is said to be oscillatory if it admits a solution \(\{x_ k\}^ \infty_ 0\) with the property that for any \(N\geq 1\), there exists an \(n\geq N\), such that \(x_ kx_{k+1}\
Cheng, Sui Sun +2 more
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Oscillation Criteria for Semilinear Equations in General Domains
Canadian Mathematical Bulletin, 1976Oscillation theory for nonlinear ordinary differential equations has been extensively developed in recent years by several authors. We refer the reader to the recent paper by Noussair and Swanson, [2], where an extensive bibliography may be found. The situation is somewhat different for the case of second order partial differential equations, an area ...
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Part Iv—Selection of Treatment: Anatomic Considerations and Criteria
Ca-A Cancer Journal for Clinicians, 1962Charles M Norris +2 more
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Proctosigmoidoscopy—Age Criteria for Examination in the Asymptomatic Patient
Ca-A Cancer Journal for Clinicians, 1975John A Coller +2 more
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