1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2(O, +∞) into Lt2q(O, ∞), v>2. When v=N-1...1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2(O, +∞) into Lt2q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1(Rn)→LQ(RN). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|l-1u+f(u) is lower then |u|v+3/v-1 i.e.展开更多
By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=...By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=λNH,with a 0-Dirichlet boundary condition on the unit ball.According to the behavior of H near 0,we obtain the global structure of sign-changing radial spacelike graphs for this problem.展开更多
We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).展开更多
In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x...In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.展开更多
In this paper,we have investigated the asymptotic behavior of nodal solutions of semilinear elliptic equations in R n. We conclude more precise and extensive results and give the expression of asymptotic behavior near...In this paper,we have investigated the asymptotic behavior of nodal solutions of semilinear elliptic equations in R n. We conclude more precise and extensive results and give the expression of asymptotic behavior near ∞ more detail than that of [3]-[5].展开更多
In this article, we establish the existence of a sign-changing solution and two sign- constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained mini...In this article, we establish the existence of a sign-changing solution and two sign- constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained minimization on appropriate Nehari manifolds.展开更多
We consider the boundary value problem△u+︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any po...We consider the boundary value problem△u+︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=(λcos^2Л(1-1)/m,λsin 2Л(1-1)/m,1=2,…,m+1such that as p goes to +∞ ,p︳x︳2α︳up︳p-1 up→8Лe(1+α)(1+α)δ0+∑^m+1δ_1=28Лe(-1)l-1δql,whereλ∈(0, 1), m is an odd number with(1+α)(m+2) -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.展开更多
In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explici...In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explicit solutions to an interesting class of nonlinear BSDEs,including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing.Moreover,we show its applications in PDEs and contingent pricing in an incomplete market.展开更多
文摘1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2(O, +∞) into Lt2q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1(Rn)→LQ(RN). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|l-1u+f(u) is lower then |u|v+3/v-1 i.e.
基金Research supported by NNSF of China(11871129)Xinghai Youqing funds from Dalian University of Technology+1 种基金NSF of Liaoning Province(2019-MS-109)HSSF of Chinese Ministry of Education(20YJA790049).
文摘By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=λNH,with a 0-Dirichlet boundary condition on the unit ball.According to the behavior of H near 0,we obtain the global structure of sign-changing radial spacelike graphs for this problem.
基金supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
文摘We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).
文摘In this paper,we study the existence of localized nodal solutions for Schrodinger-Poisson systems with critical growth{−ε^(2)Δv+V(x)v+λψv=v^(5)+μ|v|^(q−2)v,in R^(3),−ε^(2)Δψ=v^(2),in R^(3);v(x)→0,ψ(x)→0as|x|→∞.We establish,for smallε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal term φu(x)=1/4π∫R^(3)u^(2)(y)/|x−y|dy.Our results improve and extend related ones in the literature.
文摘In this paper,we have investigated the asymptotic behavior of nodal solutions of semilinear elliptic equations in R n. We conclude more precise and extensive results and give the expression of asymptotic behavior near ∞ more detail than that of [3]-[5].
文摘In this article, we establish the existence of a sign-changing solution and two sign- constant solutions for nonlinear nonlocal problem involving the BO-ZK operator on bounded domain. Our main tool is constrained minimization on appropriate Nehari manifolds.
基金Supported by the National Natural Science Foundation of China(No.11171214)
文摘We consider the boundary value problem△u+︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=(λcos^2Л(1-1)/m,λsin 2Л(1-1)/m,1=2,…,m+1such that as p goes to +∞ ,p︳x︳2α︳up︳p-1 up→8Лe(1+α)(1+α)δ0+∑^m+1δ_1=28Лe(-1)l-1δql,whereλ∈(0, 1), m is an odd number with(1+α)(m+2) -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.
基金This paper was originally exhibited in 2020(arXiv:2006.00222)。
文摘In this paper,we investigate a class of nonlinear backward stochastic differential equations(BSDEs)arising from financial economics,and give the sign of corresponding solution.Furthermore,we are able to obtain explicit solutions to an interesting class of nonlinear BSDEs,including the k-ignorance BSDE arising from the modeling of ambiguity of asset pricing.Moreover,we show its applications in PDEs and contingent pricing in an incomplete market.