Haishen Lü

Positive radial solutions for a quasilinear system

In this article, general existence theorems are presented for a quasilinear system We obtain some existence theorems by a simple application of the Schauder fixed-point theorem and degree theory. We do not require conditions of the nonlinearity f, g at zero or at infinity, and we do not need upper bounds for p, q involving the dimension n. We study the case where problem (P) is not of variational type.

A positive solution for singular discrete boundary value problems with sign-changing nonlinearities

This paper presents new existence results for the singular discrete boundary value problem −Δ2u(k−1)=g(k,u(k))

Positive solutions for Dirichlet problems of singular quasilinear elliptic equations via variational methods

This paper studies the existence and multiplicity of positive solutions of the following problem: where Ω⊂ R N ( N ≥3) is a smooth bounded domain, , 1 p N , and 0 α p - 1 p * - 1 ( p * = Np /( N - p )) and 0 γ N + (( β + 1)( p - N )/ p ) are three constants. Also δ( x ) = dist( x , ∂Ω), a ∈ L p and λ λ is small enough.

A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian

This paper studies the boundary value problem (φp(u ′))′ + q(t)(f(u) + g(u)) = 0 (0 < t < 1) u(0) = u(1) = 0 ) in the case p > 1. A necessary and sufficient condition for the existence of C[0, 1] positive solutions and a sufficient condition for the existence of C[0, 1] positive solutions are presented.

An eigenvalue interval of solutions for a singular discrete boundary value problem with sign changing nonlinearities

In this paper, we establish the existence of an eigenvalue interval of solutions to the singular discrete boundary value problem where our nonlinearity may be singular in its dependent variable and is allowed to change sign.

Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory

We present new existence results for singular discrete initial and boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.

An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities

This paper studies the eigenvalue interval for the singular boundary value problem , where may be singular at ,  , and may change sign and be superlinear at . The approach is based on an approximation method together with the theory of upper and lower solutions.

An existence theorem for singular boundary value problems with sign changing nonlinearities

In this paper, we consider the singular boundary value problem -1ppu′′=f(t,u,pu′),0<t<1,limt→0+p(t)u′(t)=0=u(1). Under the assumption that f has the singularity at u = 0 and t = 1, we present sufficient conditions for the existence of a nonnegative solution of this problem with the method of upper and lower solutions.