This paper discuss the existence of bifurcation point of positive solutions for the fully nonlinear elliptic equations involving super-critical Soboley exponent which include semilinear, MongeAmpere and Hessian equati...This paper discuss the existence of bifurcation point of positive solutions for the fully nonlinear elliptic equations involving super-critical Soboley exponent which include semilinear, MongeAmpere and Hessian equations as its examples, by setting abstract bifurcation theorem via the topological degree theory.展开更多
First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric soluti...First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.展开更多
文摘This paper discuss the existence of bifurcation point of positive solutions for the fully nonlinear elliptic equations involving super-critical Soboley exponent which include semilinear, MongeAmpere and Hessian equations as its examples, by setting abstract bifurcation theorem via the topological degree theory.
基金Supported by Natural Science Foundation of China (10631020, 10871061)the Grant for Ph.D Program of Ministry of Education of Chinasupported by Innovation Propject for the Development of Science and Technology (IHLB) (201098)
文摘First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.
