In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation me...In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.展开更多
The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and se...The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.展开更多
Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichle...Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.展开更多
By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monot...By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f（t, u） increases in u.展开更多
In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases ...In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.展开更多
In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, whe...In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, where Δ<em>u</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>u</em>) and Δ<em>v</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>v</em>) are the Laplacian of <em>u</em>, <span style="white-space:nowrap;"><em>λ</em> </span>is a positive parameter, Ω = {<em>x</em> ∈ R<sup><em>n</em></sup> : <em>N</em> > 2, |<em>x</em>| > <em>r</em><sub>0</sub>, <em>r</em><sub>0</sub> > 0}, let <em>i</em> = [1,2] then <em>K<sub>i</sub></em> :[<em>r</em><sub>0</sub>,∞] → (0,∞) is a continuous function such that lim<sub><em>r</em>→∞</sub> <em>k<sub>i</sub></em>(<em>r</em>) = 0 and <img src="Edit_19f045da-988f-43e9-b1bc-6517f5734f9c.bmp" alt="" /> is The external natural derivative, and <img src="Edit_3b36ed6b-e780-46de-925e-e3cf7c6a125f.bmp" alt="" />: [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of <em>f </em>with a) <em>f<sub>i </sub></em>> 0, b) <em>f<sub>i </sub></em>< 0, and c) <em>f<sub>i </sub></em>= 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings. </p>展开更多
The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,whe...The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,where r=x 2 1+...+x 2 n,n≥1.u=(u 1,...,u m),p(r)f(u)=(p 1(r)f 1(u),...,p m(r)f m(u)), and p(r) may be singular at r=A or r=B,f may be singular at u=0.展开更多
In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at ...In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.展开更多
基金Supported by National Natural Science Foundation of China(11071198)
文摘In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.
文摘The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.
文摘Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
基金The project was supported by NNSF of China (10371116)
文摘By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f（t, u） increases in u.
基金supported by JSPS Grant-in-Aid for Scientific Research(C)(15K04970)
文摘In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.
文摘In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, where Δ<em>u</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>u</em>) and Δ<em>v</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>v</em>) are the Laplacian of <em>u</em>, <span style="white-space:nowrap;"><em>λ</em> </span>is a positive parameter, Ω = {<em>x</em> ∈ R<sup><em>n</em></sup> : <em>N</em> > 2, |<em>x</em>| > <em>r</em><sub>0</sub>, <em>r</em><sub>0</sub> > 0}, let <em>i</em> = [1,2] then <em>K<sub>i</sub></em> :[<em>r</em><sub>0</sub>,∞] → (0,∞) is a continuous function such that lim<sub><em>r</em>→∞</sub> <em>k<sub>i</sub></em>(<em>r</em>) = 0 and <img src="Edit_19f045da-988f-43e9-b1bc-6517f5734f9c.bmp" alt="" /> is The external natural derivative, and <img src="Edit_3b36ed6b-e780-46de-925e-e3cf7c6a125f.bmp" alt="" />: [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of <em>f </em>with a) <em>f<sub>i </sub></em>> 0, b) <em>f<sub>i </sub></em>< 0, and c) <em>f<sub>i </sub></em>= 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings. </p>
基金The work was supported by NNSF(1 9771 0 0 7) of China
文摘The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,where r=x 2 1+...+x 2 n,n≥1.u=(u 1,...,u m),p(r)f(u)=(p 1(r)f 1(u),...,p m(r)f m(u)), and p(r) may be singular at r=A or r=B,f may be singular at u=0.
文摘In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.
基金Supported by the Science Foundationof Nanjing Normal University(No. 2003SXXXGQ2B37)the Science Foundation of 211En gineering and the Science Foundation of Jiangsu Province Educational Department(No. 04KJB110062).
文摘研究了拟线性椭圆型方程组div( um-2 u)=p( x )f(v), div( vn-2 v)=q( x)g(u)在RN上爆破整体正对称解的存在性和解集的性质,其中f和g在(0,∞ )上是正的递增函数.本文结果是新的且推广了所知结果.
