Nonoscillation of half‐linear dynamic equations on time scales
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DOI: 10.1002/mma.7304
Abstract: The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide… read more here.
Keywords: dynamic equations; time; nonoscillation half; equations time ... See more keywords
q‐regular variation and the existence of solutions of half‐linear q‐difference equation
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DOI: 10.1002/mma.7570
Abstract: The half‐linear q‐difference equation Dq(p(t)Φ(Dq(x(t))))+r(t)Φ(x(qt))=0,t∈qℕ0={qn:n∈ℕ0},q>1, where Φ(x)=|x|αsgnx , α>0,p:qℕ0→(0,∞),r:qℕ0→ℝ , is analyzed in the framework of q‐regular variation. Necessary and sufficient conditions for the existence of q‐regularly varying solutions are given, under the assumption that… read more here.
Keywords: regular variation; half linear; linear difference; difference equation ... See more keywords
Properties of Kneser’s solution for half-linear third order neutral differential equations
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DOI: 10.1007/s10474-017-0721-7
Abstract: AbstractWe examine properties of positive solutions of the third order differential equation with advanced argument in neutral term of the form $$(a(t)(b(t)(z'(t))^{\alpha})')'+q(t)y^{\alpha}(t)=0,$$(a(t)(b(t)(z′(t))α)′)′+q(t)yα(t)=0,where $${z(t)=y(t)+p(t)y(\sigma(t))}$$z(t)=y(t)+p(t)y(σ(t)) . They show that the positive solutions are in fact Kneser type… read more here.
Keywords: order; kneser solution; third order; half linear ... See more keywords
Oscillation and non-oscillation criteria for linear and half-linear difference equations
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DOI: 10.1016/j.jmaa.2017.03.012
Abstract: Abstract We find very general classes of linear and half-linear difference equations which are conditionally oscillatory. We identify the critical oscillation constant whose value implies the oscillation or non-oscillation of studied equations. Our results are… read more here.
Keywords: difference equations; oscillation non; oscillation; linear half ... See more keywords
Oscillation of a second order half-linear difference equation and the discrete Hardy inequality
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DOI: 10.14232/ejqtde.2017.1.43
Abstract: In local terms on finite and infinite intervals we obtain necessary and sufficient conditions for the conjugacy and disconjugacy of the following second order half-linear difference equation ∆(ρi|∆yi|∆yi) + vi|yi+1|yi+1 = 0, i = 0,… read more here.
Keywords: order half; second order; linear difference; half linear ... See more keywords
Nonoscillatory solutions of planar half-linear differential systems: a Riccati equation approach
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DOI: 10.14232/ejqtde.2018.1.92
Abstract: In this paper an attempt is made to depict a clear picture of the overall structure of nonoscillatory solutions of the first order half-linear differential system x′ − p(t)φ1/α(y) = 0, y′ + q(t)φα(x) =… read more here.
Keywords: planar half; solutions planar; linear differential; nonoscillatory solutions ... See more keywords
Criteria for Oscillation of Half-Linear Functional Differential Equations of Second-Order
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DOI: 10.3390/axioms11120719
Abstract: The present article aims to establish more effective criteria for testing the oscillation of a class of functional differential equations with delay arguments. In the non-canonical case, we deduce some improved monotonic and asymptotic properties… read more here.
Keywords: studied equation; criteria oscillation; oscillation half; half linear ... See more keywords
Lyapunov-type inequalities for certain higher-order half-linear differential equations
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DOI: 10.7153/jmi-2019-13-82
Abstract: In this paper, we will establish some new Lyapunov-type inequalities for some higherorder half-linear differential equations with anti-periodic boundary conditions. Our results not only improve the results in [9] for some cases, but also extend… read more here.
Keywords: lyapunov type; linear differential; half linear; differential equations ... See more keywords