Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:214

Article

Bonorino, LP ; Brietzke, EHM ; Lukaszczyk, JP ; Taschetto, CA

关键词: period function;    monotonicity;    homogeneous solution;    semilinear elliptic equation;    free boundary problem;   

DOI  :  10.1016/j.jde.2004.08.007

来源: Elsevier

【 摘 要 】

In this work we study the period function T of solutions to the conservative equation x(n) (t) + f (x (t)) = 0. We present conditions on f that imply the monotonicity and convexity of T. As a consequence we obtain the criterium established by C. Chicone and find conditions easier to apply. We also get a condition obtained by Cima, Gasull and Manosas about monotonicity and, following some of their calculations, present results on the period function of Hamiltonian systems where H(x, y) = F(x) + n(-1) vertical bar y vertical bar(n). Using the monotonicity of T, we count the homogeneous solutions to the semilinear elliptic equation Delta u = gamma u(gamma-1) in two dimensions. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free