In this paper,the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and diffusion suppressed by convection-div(|x|^(α)|■u|^(p-2)■u)+λ^(1)/|x|β|■u|^(p-2)■u·x=...In this paper,the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and diffusion suppressed by convection-div(|x|^(α)|■u|^(p-2)■u)+λ^(1)/|x|β|■u|^(p-2)■u·x=|x|^(γ)g(|x|)in B{0}subject to nonlinear Robin boundary value condition|x|^(α)|■u|^(p-2)■u·n=A-ρu on■B,whereλ>0,B■RN(N≥2)is the unit ball centered at the origin,α>0,p>1,β∈R,γ>-N,g∈C(0,1])with g(0)>0,A∈R,ρ>0 and n is the unit outward normal.The same problem with diffusion promoted by convection,namely λ≤0,has already been discussed by the last two authors(Song-Yin(2012)),where the existence,nonexistence and classification of singularities for solutions are presented.Completely different from[Song,H.J.and Yin,J.X.,Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection,Math.Meth.Appl.Sci.,35,2012,1089-1100],in the present caseλ>0,namely the diffusion is suppressed by the convection,non-singular solutions are not only existent but also may be infinite which vary according only to the values of solutions at the isolated singular point.At the same time,the singular solutions may exist only if the diffusion dominates the convection.展开更多
In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Mo...In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.展开更多
The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.
In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u...In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^＊=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ （0, μ0）, the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.展开更多
The author proves that there exist three solutions u(0), u(1) and u(2) in the following problem [GRAPHICS] where some conditions are imposed on Q and f. Here, 0 < u(0) < u(1), u(2) changes sign.
This paper is concerned with Neumann problem for semilinear elliptic equations involving Sobolev critical exponents with limit nonlinearity in boundary condition. By critical point theory and dual variational principl...This paper is concerned with Neumann problem for semilinear elliptic equations involving Sobolev critical exponents with limit nonlinearity in boundary condition. By critical point theory and dual variational principle, the author obtains the existence and multiplicity results.展开更多
By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-conca...By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.展开更多
We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-...We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-1)-superlinear or asymptotically (p-1)-linear at infinity.Some existence results for multiple nontrivial solutions are established by using variational methods combined with the Morse theory.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12171166,11601200,11771156,11861038,12161045,12026220)。
文摘In this paper,the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and diffusion suppressed by convection-div(|x|^(α)|■u|^(p-2)■u)+λ^(1)/|x|β|■u|^(p-2)■u·x=|x|^(γ)g(|x|)in B{0}subject to nonlinear Robin boundary value condition|x|^(α)|■u|^(p-2)■u·n=A-ρu on■B,whereλ>0,B■RN(N≥2)is the unit ball centered at the origin,α>0,p>1,β∈R,γ>-N,g∈C(0,1])with g(0)>0,A∈R,ρ>0 and n is the unit outward normal.The same problem with diffusion promoted by convection,namely λ≤0,has already been discussed by the last two authors(Song-Yin(2012)),where the existence,nonexistence and classification of singularities for solutions are presented.Completely different from[Song,H.J.and Yin,J.X.,Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection,Math.Meth.Appl.Sci.,35,2012,1089-1100],in the present caseλ>0,namely the diffusion is suppressed by the convection,non-singular solutions are not only existent but also may be infinite which vary according only to the values of solutions at the isolated singular point.At the same time,the singular solutions may exist only if the diffusion dominates the convection.
文摘In this paper,we consider an asymptotically linear second-order ordinary differential system with Dirchlet boundary value conditions. Under some conditions,we show the multiplicity of solutions to the system by the Morse theory and an index theory.
文摘The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.
基金Supported by NSFC (10571069 and 10631030) the Lap of Mathematical Sciences, CCNU, Hubei Province, China
文摘In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p＆q-Laplacian type involving the critical Sobolev exponent：{-△pu-△qu=│u│^p＊-2u＋μ│u│^r-2u in Ω u│δΩ=0,where Ω belong to R^N is a bounded domain,N〉p,p^＊=Np/N-p is the critical Sobolev exponent and μ 〉0. We prove that if 1 〈 r 〈 q 〈 p 〈 N, then there is a μ0 〉 0, such that for any μ∈ （0, μ0）, the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.
文摘The author proves that there exist three solutions u(0), u(1) and u(2) in the following problem [GRAPHICS] where some conditions are imposed on Q and f. Here, 0 < u(0) < u(1), u(2) changes sign.
文摘This paper is concerned with Neumann problem for semilinear elliptic equations involving Sobolev critical exponents with limit nonlinearity in boundary condition. By critical point theory and dual variational principle, the author obtains the existence and multiplicity results.
基金supported by the Foundation of Shanghai Municipal Education Commission (No. 06DZ004).
文摘By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.
基金This research is supported by the NSFC(Nos.11661070,11764035 and 11571176).
文摘We investigate a fractional p-Laplacian equation with right-hand-side nonlinearity which exhibits (p-1)-sublinear term of the formλ|u|q-2,q < p (concave term),and a continuous term f(x,u) which is respectively (p-1)-superlinear or asymptotically (p-1)-linear at infinity.Some existence results for multiple nontrivial solutions are established by using variational methods combined with the Morse theory.
