In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are cont...In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.展开更多
We have proved generalized Hahn-Banach theorem by using the concept of efficient for K-convex multifunction and K-sublinear multifunction in partially ordered locally convex topological vector space.
Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex compos...Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.展开更多
In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equati...In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.展开更多
In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a cla...In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.展开更多
This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x))=b(x)f(u(x)),x∈Ω,whereΩis a strictly(k-1)-convex and bounded smooth domain in Rn,b∈C∞(Ω)is positive inΩ,but may be v...This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x))=b(x)f(u(x)),x∈Ω,whereΩis a strictly(k-1)-convex and bounded smooth domain in Rn,b∈C∞(Ω)is positive inΩ,but may be vanishing on the boundary.Under a new structure condition on f at infinity,the author studies the refined boundary behavior of such solutions.The results are obtained in a more general setting than those in[Huang,Y.,Boundary asymptotical behavior of large solutions to Hessian equations,Pacific J.Math.,244,2010,85–98],where f is regularly varying at infinity with index p>k.展开更多
基金supported by the National Natural Science Foundation of China (11961060)the Graduate Research Support of Northwest Normal University (2021KYZZ01032)。
文摘In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.
文摘We have proved generalized Hahn-Banach theorem by using the concept of efficient for K-convex multifunction and K-sublinear multifunction in partially ordered locally convex topological vector space.
基金Supported by the Natural Science Foundation of Fujian Province（S0650021）
文摘Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function.The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied.A general approach for studying duality in vector optimization problems is presented.
文摘In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equations and establish an existence result.
文摘In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we obtain the optimal concavity of some Hessian operators and then establish the C2 a priori estimate for a class of prescribed σ2 curvature measure equations.
基金the National Natural Science Foundation of China(No.11571295)RP of Shandong Higher Education Institutions(No.J17KA173)。
文摘This paper is concerned with strictly k-convex large solutions to Hessian equations Sk(D2u(x))=b(x)f(u(x)),x∈Ω,whereΩis a strictly(k-1)-convex and bounded smooth domain in Rn,b∈C∞(Ω)is positive inΩ,but may be vanishing on the boundary.Under a new structure condition on f at infinity,the author studies the refined boundary behavior of such solutions.The results are obtained in a more general setting than those in[Huang,Y.,Boundary asymptotical behavior of large solutions to Hessian equations,Pacific J.Math.,244,2010,85–98],where f is regularly varying at infinity with index p>k.
