A Nonexistence Result for Choquard-Type Hamiltonian System

In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity , when , , , , , and , where and denotes the convolution in .

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt-Δu-Δut-Δutt+∫^t0g(t-s)Δu(s)ds+ut|ut|^m2-=u|u|^p-2 with acoustic boundary conditions.Under some appropriate assumption on relaxation function g and the initial data,we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

NONEXISTENCE AND SYMMETRY OF SOLUTIONS TO SOME FRACTIONAL LAPLACIAN EQUATIONS IN THE UPPER HALF SPACE

In this article, we consider the fractional Laplacian equation {（-△）α/2u=k（x）f（u）,x∈Rn＋, u=0, x Rn＋, where 0 〈α 〈 2,En＋：= {x = （x1,x2,… ,xn）｜xn〉 0}. When K is strictly decreasing with respect to ｜x＇｜, the symmetry of positive solutions is proved, where x＇ = （x1, x2,…, xn-1） ∈Rn- 1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.

NONEXISTENCE OF GLOBAL SOLUTIONS OF NONLINEAR HYPERBOLIC EQUATION WITH MATERIAL DAMPING

Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN

In this paper, we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian. We obtain some extem sion of results of Weissler who considered the case α = 1, and h ≡ 1.

Nonexistence of Nontrivial Solutions with Decay Order for a Biharmonic P-Laplacian Equation and System

We use the Morawetz multiplier to show that there are no nontrivial solutions of certain decay order for a biharmonic equation with a p-Laplacian term and a system of coupled biharmonic equations with p-Laplacian terms in the entire Euclidean space.

OPTIMAL SUMMATION INTERVAL AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A DISCRETE SYSTEM

In this paper, we are concerned with properties of positive solutions of the following Euler-Lagrange system associated with the weighted Hardy-Littlewood-Sobolev inequality in discrete form{uj =∑ k ∈Zn vk^q/（1 ＋ ｜j｜）^α（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^β,（0.1）vj =∑ k ∈Zn uk^p/（1 ＋ ｜j｜）^β（1 ＋ ｜k- j｜）^λ（1 ＋ ｜k｜）^α,where u, v 〉 0, 1 〈 p, q 〈 ∞, 0 〈 λ 〈 n, 0 ≤α ＋ β≤ n- λ,1/p＋1〈λ＋α/n and 1/p＋1＋1/q＋1≤λ＋α＋β/n：=λ^-/n. We first show that positive solutions of（0.1） have the optimal summation interval under assumptions that u ∈ l^p＋1（Z^n） and v ∈ l^q＋1（Z^n）. Then we show that problem（0.1） has no positive solution if 0 〈λˉ pq ≤ 1 or pq 〉 1 and max{（n-λ^-）（q＋1）/pq-1,（n-λ^-）（p＋1）/pq-1} ≥λ^-.

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM

In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time.

The Nonexistence of Global Solutions for a Time Fractional Schrodinger Equation with Nonlinear Memory

In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.

Nonexistence of the Quasi-harmonic Spheres and Harmonic Spheres into Certain Manifold

We mainly study the nonexistence of quasi-harmonic spheres and harmonic spheres into spheres of any dimension which omits a neighbourhood of totally geodesic submanifold of co-dimension 2.We will show that such target admits no quasi-harmonic spheres and harmonic spheres.

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily applied to the well-known Lienard equation x+f(x) x +g(x) =0, and substantially extend and improve some known results.

Existence and Nonexistence of Nontrivial Weak Solution for a Class of General Capillarity Systems

The aim of this paper is to study the nonexistence and existence of nonnegative, nontrivial weak solution for a class of general capillarity systems. The proofs rely essentially on the minimum principle combined with the mountain pass theorem.

Nonexistence of a Globally Stable Supersonic Conic Shock Wave for the Steady Supersonic Isothermal Euler Flow

In this paper, for the full Euler system of the isothermal gas, we show that a globally stable supersonic conic shock wave solution does not exist when a uniform supersonic incoming flow hits an infinitely long and curved sharp conic body.

Nonexistence and Longtime Behaviors of Solutions to a Class of Nonlinear Degenerate Parabolic Equations Not in Divergence Form

In this paper, we study the nonexistence and longtime behavior of weak solution for the degenerate parabolic equation σtun=umdiv（｜▽um｜p-2▽um）＋γ｜▽um｜p＋βun with zero boundary condition. Blow-up time is derived when the blow-up does occur.

Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

In this paper,we consider the following semilinear elliptic equation:■whereΩis an exterior domain in R^N with N≥3,h:Ω×R^+→R is a measurable function,and derive optimal nonexistence results of positive supersolutions.Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential.We also establish sharp nonexistence results of positive supersolutions to an elliptic system.

The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption

The paper proves the nonexistence of the solution for the following Cauchy problem{ut=div(|■u^m|(p-2■u^(m)))^-λu^(q),u(x,0)=δ(x),(x,t)∈S_(T)=R^(N)×(0,T),x∈R^(N),under some conditions on m,p,q,λ,whereδis Dirac function.

On Conditions of the Nonexistence of Solutions of Nonlinear Equations with Data from Classes Close to L

We establish conditions of the nonexistence of weak solutions of the Dirich- let problem for nonlinear elliptic equations of arbitrary even order with some right- hand sides from Lm where m ~ 1. The conditions include the requirement of a certain closeness of the parameter m to 1.

Existence and Nonexistence of Positive Solutions to a Singular p-Laplacian Differential Equation

In this paper we give a necessary and sufficient condition for the existence of positive solutions for the one-dimensional singular p-Laplacian differential equation. The methods used to show existence rely on upper-lower solutions method and compactness techniques, while the methods used to prove nonexistence are based on monotone techniques and scaling arguments.