临界增长条件下一类半线性椭圆方程解的存在性

用变分方法研究了半线性椭圆方程Dirichlet迫值同题-△μ=f(x,μ） h（x）对几乎所有的x∈Ω，μ=0在δΩ上解的存在性，在临界增长情况下得到了所解的一个存在性定理．     

On semilinear elliptic equations with sublinear and superlinear nonlinearities in rN

The existence of infinitely many solutions for the equation     

R~N上一类拟线性椭圆型方程弱解的多重性

在R~N上研究一类拟线性椭圆型方程,借助不光滑泛函的临界点理论和山路引理.得到该问题具有无穷多个弱解.     

Existence of solutions for the critical elliptic system with inverse square potentials

Let Ω ? 0 be an open bounded domain in R ^N (N ≥ 3) and $2^* (s) = \tfrac{{2(N - s)}} {{N - 2}}$ , 0 < s < 2. We consider the following elliptic system of two equations in H ₀ ¹ (Ω) × H ₀ ¹ (Ω): $$- \Delta u - t\frac{u} {{\left| x \right|^2 }} = \frac{{2\alpha }} {{\alpha + \beta }}\frac{{\left| u \right|^{\alpha - 2} u\left| v \right|^\beta }} {{\left| x \right|^s }} + \lambda u, - \Delta v - t\frac{v} {{\left| x \right|^2 }} = \frac{{2\beta }} {{\alpha + \beta }}\frac{{\left| u \right|^\alpha \left| v \right|^{\beta - 2} v}} {{\left| x \right|^s }} + \mu v,$$ where λ, µ > 0 and α, β > 1 satisfy α + β = 2*(s). Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions.     

全空间上半线性椭圆方程的正解

采用域扩线技巧与广义Mountain-Pass引理相结合的方法,给出了全空间上方程－Δu mu=u^p-1u的正确的存在性和光滑性。     

Solutions for a singular critical growth problem with a weight

In this paper, we consider some semilinear elliptic equations with Hardy potential. By using linking theorem in [P. Rabinowitz, Minimax Methods in Critical Points Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986] and analyzing the effect of nonlinearities, we establish the existence of nontrivial solutions.     

A semilinear elliptic equation with double resonance

In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied.     

Solutions for semilinear elliptic equations with critical exponents and Hardy potential

In this paper, we answer affirmatively an open problem (cf. Theorem 4′ in Ferrero and Gazzola (J. Differential Equations 177 (2001) 494): Let Ω∋0 be an open-bounded domain, Ω⊂RN(N?5) and assume that , then, for all λ>0 there exists a nontrivial solution with critical level in the range for the problem in Ω; u=0 on ∂Ω.     

Local superlinearity and sublinearity for indefinite semilinear elliptic problems

In this paper the usual notions of superlinearity and sublinearity for semilinear problems like −Δu=f(x,u) are given a local form and extended to indefinite nonlinearities. Here f(x,s) is allowed to change sign or to vanish for s near zero as well as for s near infinity. Some of the well-known results of Ambrosetti-Brézis-Cerami are partially extended to this context.     

Solutions to critical elliptic equations with multi-singular inverse square potentials

Let Ω be an open-bounded domain in R^N(N?3) with smooth boundary ∂Ω. We are concerned with the multi-singular critical elliptic problem

     

ON INDEFINITE SUBLINEAR ELLIPTIC EQUATIONS

The existence, uniqueness, multiplicity and asymptotic behavior of the solutions to the equation are studied by means of variational and sub-sup-solution methods, where 0 ＜ q ＜ p ＜1, Ω RN with N ＞ 3 is a smooth bounded domain, a, b ∈ L∞(Ω) and λ ∈ R1 is aparameter.     

一类半线性椭圆方程的正径向解

本文以关于非线性全连续算子的锥不动点定理为工具，研究半线性椭圆边值问题上Δu λa(|x|)u f(|x|,u)=0(x∈Ω)，u|=0及Δu λf(|x|,u)=0(x∈Ω)，u|=0．在不假定f单调的情况下，本文得出了上述问题存在正径向解的若干充分条件．     

Corrigendum to “Coexistence states of a Holling type-II predator-prey system” [J. Math. Anal. Appl. 369 (2) (2010) 555-563]

We present the asymptotic behavior of the coexistence states near the point of bifurcation from infinity of the form

(0.1)