01258nas a2200145   4500008004100000245010200041210006900143260008500212300001400297490000700311520069200318100002201010700002301032856005701055       2013                        eng d00aGeneralized Sturm-Liouville boundary conditions for first order differential systems in the plane0 aGeneralized SturmLiouville boundary conditions for first order d  bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies  a293–3250 v423 a<p>We 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.</p>1 aFonda, Alessandro1 aGarrione, Maurizio  uhttps://projecteuclid.org:443/euclid.tmna/1461248981