This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to pro...This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.展开更多
The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed ...The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.展开更多
基金the National Natural Science Foundation of China(Grant Nos.10671064,10171029)
文摘This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.
基金Supported by the National Natural Science Foundation of China (No. 10671064 and No.10971061)the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.
