Non-existence of positive radial solutions for a class of quasilinear elliptic system

In this paper, our main purpose is to establish some nonexistence results of positive radial solutions to the quasilinear ordinary differential equation system. The main results of the present paper are new and extend the previously known results.     

A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations

This paper is concerned with an operator equation Ax+Bx+Cx=x on ordered Banach spaces, where A is an increasing α-concave operator, B is an increasing sub-homogeneous operator and C is a homogeneous operator. The existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators. As applications, we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth-order two-point boundary value problems for elastic beam equations and elliptic value problems for Lane-Emden-Fowler equations.     

Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class

Let us consider the problem whether there does exist a finite-time self-similar solution of the backward type to the semilinear Keller-Segel system. In the case of parabolic-elliptic type for n?3 we show that there is no such a solution with a finite mass in the scaling invariant class. On the other hand, in the case of parabolic-parabolic type for n?2, non-existence of finite-time self-similar solutions is proved in a larger class of a finite mass with some local bounds.     

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order derivatives are taken into account, namely, the Caputo, Riemann-Liouville and Grunwald-Letnikov definitions. As a consequence, the non-existence of exact periodic solutions in a wide class of fractional-order dynamical systems is obtained. As an application, it is emphasized that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system.     

Global existence and blow-up solutions and blow-up estimates for a non-local quasilinear degenerate parabolic system

This paper deals with p-Laplacian systems

with null Dirichlet boundary conditions in a smooth bounded domain ΩR^N, where p,q>1, , and a,b>0 are positive constants. We first get the non-existence result for a related elliptic systems of non-increasing positive solutions. Secondly by using this non-existence result, blow-up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=B_R={xR^N:|x|<R}(R>0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exists globally or blow-up in finite time.     

Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term

We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle.     

Non-existence of super-additive solutions for 3-person games

The super-additive solution for 2-person Nash bargaining games (with constant threat) was defined axiomatically inPerles/Maschler [1981]. That paper contains also a study of its basic properties. In this paper we show that the axioms are incompatible even for 3-person unanimity games. This raises the problem of finding a satisfactory generalization of this solution concept to multi-person games.     

NON-EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR ELLIPTIC INEQUALITIES OF P-LAPLACIAN

In this paper,the nonexistence of positive entire solutions for div(|Du|^1-2Du)≥q(x)f(u),x∈R^N,is establisbed,where p＞1,DU=(D,u……dnu),qsR^N→(o,∞)and f2(0,∞)→(o,∞)are continuous functions.     

On the Schrödinger-Maxwell system involving sublinear terms

In this paper, we study the coupled Schrödinger-Maxwell system

(SM_λ)     

Regularity criteria for the Navier-Stokes-Landau-Lifshitz system

In this paper, we study regularity criteria for the Navier-Stokes-Landau-Lifshitz system. Using delicate estimates, the regularity criteria for smooth solution of Navier-Stokes-Landau-Lifshitz system in Besov spaces and the multiplier spaces are obtained. The Navier-Stokes-Landau-Lifshitz system is coupled system of the Navier-Stokes equation and Landau-Lifshitz system, our results generalize the related results for Navier-Stokes equation and Landau-Lifshitz system to our system.     

Non-existence of one-signed solutions for variational equations with locally amplifying potentials

In questo lavoro si considerano equazioni differenziali ordinarie del secondo ordine di tipo singolare della forma

Non-existence of one-signed solutions for variational equations with locally amplifying potentials

In questo lavoro si considerano equazioni differenziali ordinarie del secondo ordine di tipo singolare della forma

$$[g(t)G_p (u,u')]' - g(t)G_u (u, u') + g(t)f(t, u) = 0$$     

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

IntroductionIn these years, the reaction-diffusion systems of Fujita typea5 ttell as the related elliptic systemt'ith fl g RN, Tnl. n1 3 0, i = 1, 2. \vere studied by' a nu111ber of authors. The probiemsconcerning system (l) inc1ude globa1 existence and g1obal existen(.e numbers. b1ow-up. bloxv-uprates, and blow-up sets. uniqueness or nonuniqueness. et('. FOr s}'stem (2) there are problemssuch as existence or non-existence. uniqueness or nonllniqueI1ess. and so ol1. 1Ieanwhile. itseems that…     

Non-existence of a universal zero-entropy system

We prove that there does not exist a zero-entropy topological dynamical system whose set of invariant measures contains isomorphic copies of all measure-theoretic systems of entropy zero.     

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions

We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem.Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.