In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,wi...In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,with the help of a fixed point approach.We use Gronwall’s inequality on time scales,an abstract Growall’s lemma and a Picard operator as basic tools to develop our main results.To overcome some difficulties,we make a variety of assumptions.At the end an example is given to demonstrate the validity of our main theoretical results.展开更多
In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=...In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.展开更多
基金Supported by National Natural Science Foundation of China(10971046)the Project of Shandong Province Higher Educational Science and Technology Program(J09LA55)Graduate Independent Innovation Foundation of Shandong University(yzc12063)
基金supported by Talent Project of Chongqing Normal University(02030307-0040)the China Posdoctoral Science Foundation(2019M652348)+1 种基金Natural Science Foundation of Chongqing(cstc2020jcyj-msxm X0123)Technology Research Foundation of Chongqing Educational Committee(KJQN202000528,KJQN201900539)。
文摘In this article,we present the existence,uniqueness,Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales,with the help of a fixed point approach.We use Gronwall’s inequality on time scales,an abstract Growall’s lemma and a Picard operator as basic tools to develop our main results.To overcome some difficulties,we make a variety of assumptions.At the end an example is given to demonstrate the validity of our main theoretical results.
基金Supported by the National Natural Science Foundation of China(11601048) Natural Science Foundation of Chongqing(cstc2016jcyj A0181)+1 种基金 the Science and Technology Research Program of Chongqing Municipal Education Commission(KJ1703050) Natural Science Found
基金supported by NSFC(12001344)the Graduate Education and Teaching Innovation Project of Shanxi,China(2021YJJG142)+1 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0123)the Technology Research Foundation of Chongqing Educational Committee(KJQN201900539 and KJQN202000528)。
文摘In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.
