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POSITIVE ENTIRE SOLUTIONS TO SINGULAR SEMILINEAR ELLIPTIC EQUATIONS OF MIXED TYPE 被引量:1
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作者 姚妙新 《Transactions of Tianjin University》 EI CAS 1995年第1期41+38-41,共5页
In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general in... In this paper, we are concerned with positive entire solutions to elliptic equations of the form Δu+ f(x,u)= 0 x∈ RN N ≥ 3 where u →f(x,u) is not assumed to be regular near u = 0 and f(x,u) may be more general involving both singular and sublinear terms. Some sufficient conditions are given with the aid of the barrier method and ODE approach, which guarantee the existence of positive entire solutions that tend to any sufficiently large constants arbitrarily prescribed in advance. 展开更多
关键词 singular semilinear elliptic equation bounded positive entire solution barrier method
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ASYMPTOTIC SOLUTION OF SINGULAR PERTURBATION PROBLEMS FOR THE FOURTH-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS 被引量:1
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作者 苏煜城 刘国庆 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第7期637-650,共14页
In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal... In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution. 展开更多
关键词 ASYMPTOTIC SOLUTION OF singular PERTURBATION PROBLEMS FOR THE FOURTH-ORDER elliptic DIFFERENTIAL equations
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A boundary expansion of solutions to nonlinear singular elliptic equations
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作者 Huaiyu Jian Jian Lu Xu-Jia Wang 《Science China Mathematics》 SCIE CSCD 2022年第1期9-30,共22页
In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profi... In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profile of solutions at the boundary.We deal with both linear and nonlinear elliptic equations,including fully nonlinear elliptic equations and equations of Monge-Ampère type. 展开更多
关键词 boundary asymptotic expansion singular nonlinear elliptic equations Dirichlet problem
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ON SINGULAR EQUATIONS INVOLVING FRACTIONAL LAPLACIAN 被引量:3
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作者 Ahmed YOUSSFI Ghoulam OULD MOHAMED MAHMOUD 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1289-1315,共27页
We study the existence and the regularity of solutions for a class of nonlocal equations involving the fractional Laplacian operator with singular nonlinearity and Radon measure data.
关键词 fractional Laplacian singular elliptic equations measure data
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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN R^N 被引量:1
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作者 贺小明 邹文明 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期830-840,共11页
In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ|x|^2^-μ=α|x|^s^-|μ|^2*(s)-2u+βα(x)|u|^... In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ|x|^2^-μ=α|x|^s^-|μ|^2*(s)-2u+βα(x)|u|^r-2u,x∈R^n. By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α,β. 展开更多
关键词 singular elliptic equation Multiple solutions Critical Sobolev-Hardy exponent Minimax method
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EXISTENCE OF SINGULAR POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS 被引量:1
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作者 綦建刚 庄万 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 1998年第1期109-112,共4页
关键词 EXISTENCE OF singular POSITIVE SOLUTIONS OF SEMILINEAR elliptic equations
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The Ground State Solutions for Kirchhoff-Schrodinger Type Equations with Singular Exponential Nonlinearities in R^(N)
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作者 Yanjun LIU Chungen LIU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2022年第4期549-566,共18页
In this paper,the authors consider the following singular Kirchhoff-Schrodinger problem M(∫_(R^(N))|∇u|^(N)+V(x)|u|^(N)dx)(−Δ_(N)u+V(x)|u|^(N-2)u)=f(x,u)/|x|^(η)in R^(N),(P_(η))where 0<η<N,M is a Kirchhoff-... In this paper,the authors consider the following singular Kirchhoff-Schrodinger problem M(∫_(R^(N))|∇u|^(N)+V(x)|u|^(N)dx)(−Δ_(N)u+V(x)|u|^(N-2)u)=f(x,u)/|x|^(η)in R^(N),(P_(η))where 0<η<N,M is a Kirchhoff-type function and V(x)is a continuous function with positive lower bound,f(x,t)has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates,they get the existence of ground state solution for(P_(η)).Moreover,they also get the same result without the A-R condition. 展开更多
关键词 Ground state solutions singular elliptic equations Critical exponential growth Kirchhoff-Schrodinger equations singular Trudinger-Moser inequality
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ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY
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作者 JIANGHUIQIANG LINFANGHUA 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2004年第1期65-72,共8页
Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of ze... Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model. 展开更多
关键词 singular elliptic equation Poincare inequality Thin film Partial regu- larity Zero set Rupture set Hausdorff dimension
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