Oscillation for a class of neutral parabolic differential equations

AbstractSome sufficient conditions are established for the oscillation of a class of neutral parabolic differential equations of the form,∂N(u(x,t)−∑k=1rλku(x,t−ρk))∂tN−a(t)Δu+∑i=1npi(x,t)u(x,t−σi)−∑j=1mqj(x,t)u(x,t−τj)+h(t)f(u(x,t−r1),,u(x,t−rl))=0,(x,t)∈Ω×[t0,+∞)≡G,t0∈R+,where N is an odd number, Ω is a bounded domain in RM with a smooth boundary ∂Ω, and Δ is the Laplacian operation with three different boundary conditions. We obtained some new oscillatory conditions for the odd-order neutral parabolic differential equation. To some extent, our results are new oscillatory conditions, and extended some oscillatory results of some references

Oscillation and asymptotic behavior for a class of delay parabolic differential

AbstractSome comparative theorems are given for the oscillation and asymptotic behavior for a class of high order delay parabolic differential equations of the form ∂n(u(x,t)−p(t)u(x,t−τ))∂tn−a(t)△u+c(x,t,u)+∫abq(x,t,ξ)f(u(x,g1(t,ξ)),…,u(x,gl(t,ξ)))dσ(ξ)=0,(x,t)∈Ω×R+≡G, where n is an odd integer, Ω is a bounded domain in Rm with a smooth boundary ∂Ω, and △ is the Laplacian operation with three boundary value conditions. Our results extend some of those of [P. Wang, Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments, Appl. Math. Comput. 106 (1999), 163–169] substantially

Solvability of Third-Order Three-Point Boundary Value Problems

We are interested in the existence theorems for a third-order three-point boundary value problem. In the nonresonant case, using the Krasnosel’skii fixed point theorem, we obtain some sufficient conditions for the existence of the positive solutions. In addition, we focus on the resonant case, the boundary value problem being transformed into an integral equation with an undetermined parameter, and the existence conditions being obtained by the Intermediate Value Theorem

Solvability for a Fractional Order Three-Point Boundary Value System at Resonance

A class of fractional order three-point boundary value system with resonance is investigated in this paper. Using some techniques of inequalities, a completely new method is incorporated. We transform the problem into an integral equation with a pair of undetermined parameters. The topological degree theory is applied to determine the particular value of the parameters so that the system has a solution

Existence of nontrivial solutions for a class of biharmonic equations with singular potential in RN RN\mathbb{R}^{N}

Abstract In this paper, we study a class of biharmonic equations with a singular potential in RN $\mathbb{R}^{N}$. Under appropriate assumptions on the nonlinearity, we establish some existence results via the Morse theory and variational methods. We significantly extend and complement some results from the previous literature

A Model for Influence of Nuclear-Electricity Industry on Area Economy

A model for Influence of Nuclear-Electricity Industry on Area Economy is established in this paper; we obtain an existence condition of solutions. Further, the approximation conditions are also constructed; the economic aggregate will tends to the equilibriums point as time tend to infinity