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.     

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.     

Boundary blow-up solutions for a class of quasilinear elliptic equations

For a given bounded domain Ω in R ^N with smooth boundary ?Ω, we give sufficient conditions on f so that the m-Laplacian equation △ _m u = f(x, u, ?u) admits a boundary blow-up solution u ∈ W ^1,p (Ω). Our main results are new and extend the results in J.V. Concalves and Angelo Roncalli [Boundary blow-up solutions for a class of elliptic equations on a bounded domain, Appl. Math. Comput. 182 (2006), pp. 13–23]. Our approach employs the method of lower–upper solution theorem, fixed point theory and weak comparison principle.     

Transition-layer solutions of quasilinear elliptic boundary blow-up problems and dirichlet problems

We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation:

Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations

The existence and uniqueness of positive radial solutions of the equations of the type [IML0001] in B_R, p>1 with Dirichlet condition are proved for λ large enough and f satisfying a condition[IML0002] is non-decreasing on [IML0003] It is also proved that all the positive solutions in C₁ ⁰(B^R) of the above equations are radially symmetric solutions for f satisfying [IML0004] and λ large enough.     

Local existence inC b 0, 1 and blow-up of the solutions of the Cauchy Problem for a quasilinear hyperbolic system with a singular source term

In this paper we consider the Cauchy problem for the hyperbolic system

On a class of sublinear quasilinear elliptic problems

We establish existence and multiplicity of positive solutions to the quasilinear boundary value problem

where is a bounded domain in with smooth boundary , is continuous and p-sublinear at and is a large parameter.

     

Structure of positive solutions for quasilinear elliptic systems—degenerate ecological models

We study the degenerate ecological models where are positive numbers. The structure of positive solutions of the models is discussed via bifurcation theory and monotone techniques. Copyright © 2004 John Wiley & Sons, Ltd.     

Existence and uniqueness of solutions for quasilinear elliptic systems

We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.

     

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems.     

环域上一类拟线性椭圆型方程的正径向解的存在性

The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^ f‘ (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge positive radial solution on all annuli. If f(0)≤0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide.     

一类椭圆系统正径向解的存在性

通过考察函数f,g在端点处的性质证明了一类非线性椭圆系统在环域上的正径向解的存在性.     

Behavior of positive radial solutions for quasilinear elliptic equations

We establish a necessary and sufficient condition so that positive radial solutions to 0, \end{equation*}"> having an isolated singularity at , behave like a corresponding fundamental solution. Here, and are continuous functions satisfying some mild growth restrictions.

     

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.     

Existence of entire explosive positive radial solutions of sublinear elliptic systems

1 Formulation Existence and nonexistence of solutions of the quasilinear elliptic systemhas received much attention recently (see, for example, [1-61).Problem (1) arises in the theory of quasiregular and quasiconformal mappings or in thestudy of non-Newtonian fluids. In the.latter case, the quantity (P, q) is a characteristic of themedium. Media with p > 2 and q > 2 are called dilatant fluids and those with p < 2 and q < 2are called pseudoplastics. If p = q = 2, they are Newtonian fluids.Whe…     

Boundary blow-up solutions for a cooperative system of quasilinear equation

We study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear elliptic system

     

Properties of positive solutions to a nonlinear parabolic problem

This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.     

Global nonexistence of positive initial energy solution for coupled quasilinear system

In this paper, we consider global nonexistence of a solution for coupled quasilinear system with damping and source under Dirichlet boundary condition. We obtain a global nonexistence result of solution by using the perturbed energy method, where the initial energy is assumed to be positive. Copyright © 2017 John Wiley & Sons, Ltd.