Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ N

In this paper, by the Alexandrov-Serrin method of moving plane combined with integral inequalities, we prove some new Liouville type results for positive solution of semilinear elliptic system in the whole space ? ^N .     

Hölder Continuity of Solutions for Quasilinear Elliptic Equations with Gradient Terms and Measures

Potential Analysis - We consider quasi-linear second order elliptic differential equations with gradient terms and study Hölder continuity of solutions of the equation. Also, as an application...     

Lq Interior Estimates of the Gradient for Weak Solutions of Quasilinear Elliptic Equations

The authors present a new proof of L^q interior estimates of the gradient for weak solutions of a quasilinear elliptic equation of p-Laplacian type.     

Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains

Sufficient conditions for the existence of positive solutions to a class of quasilinear elliptic equations in two-dimensional exterior domains are given.     

Existence and Multiplicity of Solutions for a Class of Quasilinear Elliptic Equations with Exponential Growth北大核心CSCD

本文研究一类具有次临界多项式增长或次临界指数型(临界指数型)增长的(p,2)-拉普拉斯方程一个正解及无穷多非平凡解的存在性,运用山路定理及喷泉定理,得到了拉普拉斯方程非平凡解的一些存在性结果.     

Elliptic problems involving the p-Laplacian in ℝN with locally Lipschitz functional

We study the existence of infinitely many weak solutions for the elliptic type equation via a general nonsmooth critical point theorem.     

Continuity of Weak Solutions for Quasilinear Parabolic Equations with Strong Degeneracy

The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288].     

Non-existence Results for Quasilinear Elliptic Equations in Unbounded Domains

In the middle of 1980s,Ni＆Serrin,Grads,Ni ＆Nirenberg,established a generalized iueqnality for the sphelrical symmetry Solutions of quasilinear elliptic equations diV[A(|Du|)] ,f(u)=0,χ∈~n (1) By using this inequality,the results that do not exist spherical symmetry solution can be Proved.In order to study the non-existence of the nonspherical symmetry Solutions,We must establish the Pohozaev' ideutity or inequality for general nonspherical symmetry SOlutions for the most general quasilinear Euler equations     

Boundedness of Solutions for Elliptic Variational Inequalities

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Sign-changing Solutions to Nonlinear Elliptic Equations with Hardy Potential and Critical Parameter in ℝ2

Acta Mathematicae Applicatae Sinica, English Series - In this paper, a new Hilbert space is defined which is embedded into $$W_{0}^{1, q}(Omega)$$ for 1 ≤ q < 2. By using...     

Structure of Coexistence States for a Class of Quasilinear Elliptic Systems

The structure of positive solutions of the p-Laplacian systems is discussed via bifurcation theory and monotone techniques.     

On Singular Solutions of Boundary Value Problems for Quasilinear Parabolic Equations with Absorption

The existence and nonexistence of non-trivial solutions for the boundary value problemare studied.     

Harnack’s Inequality for Quasilinear Elliptic Equations with Singular Absorption Term

Potential Analysis - In this article we study nonnegative solutions of quasilinear equation model of which is $$-triangle_{p} u+V(x) f(u)= h(x)|nabla u|^{p-1}+g(x), ,,,, p>1.$$ Under...     

Existence of Solutions for a Quasilinear Schrödinger Equation with Potential Vanishing

Acta Mathematicae Applicatae Sinica, English Series - We study the following quasilinear Schrödinger equation $$ - \Delta u + V(x)u - \Delta ({u^2})u = K(x)g(u),\,\,\,\,\,\,\,\,x \in...     

Weak Solutions to the Cahn-Hilliard Equation with Degenerate Diffusion Mobility in ℝN

This paper is concerned with a popular form of Cahn-Hilliard equation which plays an important role in understanding the evolution of phase separation. We get the existence and regularity of a weak solution to nonlinear parabolic, fourth order Cahn-Hilliard equation with degenerate mobility M(u)=u^m(1-u)^m which is allowed to vanish at 0 and 1. The existence and regularity of weak solutions to the degenerate Cahn-Hilliard equation are obtained by getting the limits of Cahn-Hilliard equation with non-degenerate mobility. We explore the initial value problem with compact support and obtain the local non-negative result. Further, the above derivation process is also suitable for the viscous Cahn-Hilliard equation with degenerate mobility.     

Infinitely Multiple Eigenvalues of The Dirichlet Problem for Quasilinear Elliptic Equations

In this paper, We consider the following Dirichlet problem for quasilinearelliptic equation ( /x_i)F_i(x,Du)=-λu-p(x,u) x∈Ω(1) u| Ω=0     

Sign-changing solutions for p-biharmonic equations with Hardy potential in ℝN

In this article, by using the method of invariant sets of descending flow, we obtain the existence of sign-changing solutions of p-biharmonic equations with Hardy potential in ?^N.     

Sign-Changing Solutions for a Class of Nonlinear Elliptic Problems

In the present paper,the author studies the existence of sign-changing solutions for nonlinear elliptic equations,which have jumping nonlinearities,and may or may not be resonant with respect to Fu(?)ik spectrum,via linking methods under Cerami condition.