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April  2000, 6(2): 475-482. doi: 10.3934/dcds.2000.6.475

Positively homogeneous equations in the plane

Alessandro Fonda 1, and  Rafael Ortega 2,

1. 

Dipartimento di Scienze Matematiche, Universita di Trieste, P.le Europa 1 34127 Trieste, Italy
2. 

Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Received  May 1999 Revised  October 1999 Published  January 2000

We prove the multiplicity of periodic solutions to second order ordinary differential equations in $\mathbb R^2$ with nonlinearities crossing the two first eigenvalues of the differential operator.
Keywords: periodic solutions., jumping nonlinearities, Piecewise linear equations.
Mathematics Subject Classification: 34C25, 34B1.
Citation: Alessandro Fonda, Rafael Ortega. Positively homogeneous equations in the plane. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 475-482. doi: 10.3934/dcds.2000.6.475
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