By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with p-Laplacian: ${\left({\varphi}_{p}\left({x}^{\text{'}}\right)\right)}^{\text{'}}+d/dtgradF\left(x\right)+gradG\left(x\right)=e\left(t\right)$, x(0) = x(T), x’(0) = x’(T). Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces d/dt gradF(x).

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-{\left({\varphi}_{p}\left({x}^{\text{'}}\right)\right)}^{\text{'}}+d/dtgradF\left(x\right)+g(t,x\left(t\right),x\left(\delta \left(t\right)\right)$, x’(t), x’(τ(t))) = 0, t ∈ [0,1]; $x\left(t\right)=\underline{\phi}\left(t\right),$ t ≤ 0; $x\left(t\right)=\overline{\phi}\left(t\right)$, t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).

Classical goodness of fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is suitably constructed. This randomization makes the classical tests distributional free. The power under local alternatives is investigated. Computer simulations...

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

In this paper we study two classes of delay partial difference equations with constant coefficients. Explicit necessary and sufficient conditions for the oscillation of the solutions of these equations are obtained.

A Volterra model with mutual interference
concerning integrated pest management is proposed and analyzed. By
using Floquet theorem and small amplitude perturbation method and
comparison theorem, we show the existence of a globally
asymptotically stable pest-eradication periodic solution. Further,
we prove that when the stability of pest-eradication periodic
solution is lost, the system is permanent and there exists a
locally stable positive periodic solution which arises from the
pest-eradication...

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