Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
In this paper, we construct first a new concrete example of asymmetric convex compact C 1,1-hypersurfaces in R 2n possessing precisely n closed characteristics. Then we prove multiplicity results on the closed characteristics on convex compact hypersurfaces in R 2n pinched by not necessarily symmetric convex compact hypersurfaces.
