Periodic solutions for nonlinear systems with mean curvature-like operators

Abstract

Abstract. We give an existence result for a periodic boundary value problem involving mean curvaturelike operators. Following a recent work of R. Manásevich and J. Mawhin, we use an approach based on the Leray-Schauder degree.

Nonlinear systems with mean curvature-like operators

“…In [1] and [2] we proceeded in the general spirit of Manásevich-Mawhin's ideas and we proved, as said before, an existence result for (1.1), assuming that A is the identity. We still follow here the same approach: under suitable assumptions on f , which we specify in the sequel, we apply the Leray-Schauder degree and we show (Theorem 4.1 below) that (1.1) admits a solution.…”

“…Introduction. In this paper we study the existence of periodic solutions of the nonlinear differential problem Our purpose here is to enrich some recent results obtained in [1] and [2] about problem (1.1) in the more restrictive assumption that A is the identity.…”

Subharmonic solutions of the prescribed curvature equation

“…The question of the existence of periodic solutions of (1) has received considerable attention in recent years: the existence of classical solutions has been addressed in [4,5,6,7,8,9,10] by using topological methods, whereas the existence of bounded variation solutions has been discussed in [11,12,13] by using non-smooth critical point theory. The advisability of considering bounded variation solutions, besides classical solutions, in order to have a complete picture of the solvability patterns of (1), is already evident for the autonomous equation…”

Exact number of solutions of a prescribed mean curvature equation

“…(1.1) Such type of prescribed mean curvature equations both in one and in higher dimension with various nonlinearities have been studied by many authors (see, for instance, [3][4][5][6][7]11,12,[14][15][16][17][18]). …”