Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane
KeywordsPositively homogeneous planar systems, Sturm-Liouville boundary conditions, shooting method, cone
AbstractWe study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fučík spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.
How to Cite
FONDA, Alessandro & GARRIONE, Maurizio. Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane. Topological Methods in Nonlinear Analysis [online]. 22 April 2013, T. 42, nr 2, s. 293–325. [accessed 28.3.2023].
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