Nonnegative solutions for nonlinear elliptic systems

In this paper, we show that the semilinear elliptic systems of the form

(0.1)     

Nonnegative doubly periodic solutions for nonlinear telegraph system

This paper deals with the nonnegative doubly periodic solutions for nonlinear telegraph system

     

Nonnegative doubly periodic solutions for nonlinear telegraph system with twin-parameters

In this paper, by using Krasnosel’skii fixed-point theorem and under suitable conditions, we present the existence and multiplicity of nonnegative doubly periodic solutions for the following system:

     

Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary

In this paper we perform an extensive study of the existence, uniqueness (or multiplicity) and stability of nonnegative solutions to the semilinear elliptic equation − Δu = λ u − u ^p in Ω, with the nonlinear boundary condition ∂u/∂ν = u ^r on ∂Ω. Here Ω is a smooth bounded domain of with outward unit normal ν, λ is a real parameter and p, r > 0. We also give the precise behavior of solutions for large |λ| in the cases where they exist. The proofs are mainly based on bifurcation techniques, sub-supersolutions and variational methods.      

Nonnegative solutions of an elliptic equation with a singular potential

We study the behavior of nonnegative solutions of the Dirichlet problem for a linear elliptic equation with a singular potential in the ball B = B(0,R) ⊂ R ⁿ (n ≥ 3), R ≤ 1. We find an exact condition on the potential ensuring the existence or absence of a nonnegative solution of that problem.     

Nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity

We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem

     

Exact solutions for a nonlinear model

In this paper we show new exact solutions for a type of generalized sine-Gordon equation which is obtained by constructing a Lagrange function for a dynamical coupled system of oscillators. We convert it into a nonlinear system by perturbing the potential energy from a point of view of an approach proposed by Fermi [1].     

Smoothness of solutions of a nonlinear ode

Smoothness of aC -functionf is measured by (Carleman) sequence {M _k} ₀ ; we sayfC _M [0, 1] if|f ^(k) (t)|CR ^k M _k,k=0, 1, ... withC, R>0. A typical statement proven in this paper isTHEOREM: Let u, b be two C -functions on [0, 1]such that (a) u=u ²+b, (b) |b ^(k) (t)|CR ^k (k!) , >1,k_–.Then |u^(k)(t)|C₁R^k((k–1)!),k_–.The first author acknowledges the hospitality of Mathematical Research Institute of the Ohio State University during his one month visit there in the spring of 1999     

临界增长的1-Laplace 方程的非负解

在BV 空间中研究如下一类含临界指数的1-Laplace 方程非负解的存在性:
-Div(Du/|Du|)=g(x, u)+|u|^1*-2u, x∈Ω,
其中Ω⊂R^N 为有界光滑开区域, 1^*=N/(N-1),g(x, u) 为Carathéodory 函数.     

Nonnegative radial solutions to a class of elliptic equations involving the Pucci's extremal operator

In this article we use Leray-Schauder degree to consider the existence of nonnegative radially symmetric solution for the nonlinear elliptic equation in BR, y=0 on ∂BR, where denotes the Pucci's extremal operators with parameters 0<λ?Λ and BR is the ball of radius R in RN, N?3. As an application we can obtain the results to equation , where and 0<q<p.     

Time-periodic solutions of a nonlinear wave equation

The existence of a time-periodic solution of an n-dimensional nonlinear wave equation is established with n=2 and 3.     

Polynomial solutions of a nonlinear difference equation

A class of nonlinear difference equations is considered. We show how their polynomial solutions can be computed in a systematic manner.     

Approximate solutions of a nonlinear differential equation

Approximate solutions of a nonlinear differential equation ẍ + α^mx² = β^mx^{m + 2} (m⩾1) are approximate solution is exact for a particular initial value.     

Safe solutions of a nonlinear car-following equation

A leader-follower pair of cars whose motion is subject to a non-linear delay differential equation are travelling with the same constant velocity u_I when the leader begins to change his velocity in a smooth way to the non-negative velocity u_F < u_I. Conditions are found for the response of the follower to be a safe one according to certain natural safety criteria.     

Unbounded solutions of a nonlinear parabolic equation

The article investigates the equation