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
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
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
The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem the existence,uniqueness and asymptotic behavio...The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem the existence,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.展开更多
In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential inequalities.The uniformly valid a...In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential inequalities.The uniformly valid asymptotic expansion of solution is obtained.展开更多
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.
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
文摘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.
文摘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.
基金supported by Australian Research Council(Grant No.FL130100118)National Natural Science Foundation of China(Grant Nos.11771237 and 11871432)。
文摘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.
基金Supported by the National Natural Science Foundation of China (1 0 0 71 0 4 8)
文摘The singularly perturbed Robin boundary value problems for the semilinear elliptic equation are considered.Under suitable conditions and by using the fixed point theorem the existence,uniqueness and asymptotic behavior of solution for the boundary value problems are studied.
文摘In this paper,a class of singular perturbation of nonlocal boundary value problems for elliptic partial differential equations of higher order is considered by using the differential inequalities.The uniformly valid asymptotic expansion of solution is obtained.
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11790271,12171108,12201089)Guangdong Basic and Applied basic Research Foundation(No.2020A1515011019)Innovation and Development Project of Guangzhou University and Chongqing Normal University Foundation(No.21XLB039)。
文摘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.
