Infinitely Many T-Periodic Solutions for a Problem Arising in Nonlinear Elasticity

Periodic orbits of a singular superlinear planar system

“…Assumption (H 2 ) is a typical condition to describe a strong singularity, which has been used by many researchers [7,17,19,21,24] to control the solutions which approach the singularity. Assumption (H 2 ) is also called a strong force condition (such a terminology was first introduced by Gordon in [15] as a different form, which has a slightly different meaning from our situation) in the literature [14,23,24].…”

“…We remark that the existence of periodic solutions for singular differential equations has a long history and has been studied by many researchers. See [5,7,17,19,21] and the references therein. Usually, the proof is based on either a variational approach [1,15], the method of upper and lower solutions [3,20], fixed point theorems [4][5][6]13,14,18,22] or topological degree theory [24].…”

Periodic solutions of singular nonautonomous second order differential equations

“…See for instance [3][4][5][6][7][8][9][10], [12], [14], [17], [21] and [22]. In almost all these papers the differential equation contains a friction term that does not allow the application of a variational method.…”

Solvability of the Neumann Problem in a Ball for −δu+u−v=h(|x|),v>1

“…where f is continuous on [0, ) and unbounded above, have been treated in [2] and [3], respectively for the cases of an asymptotically linear and a superlinear f. It should be remarked that in the higher dimensional case, the related problem…”