## Topological Methods in Nonlinear Analysis

### Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane

#### Abstract

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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 42, Number 2 (2013), 293-325.

Dates
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.tmna/1461248981

Mathematical Reviews number (MathSciNet)
MR3203451

Zentralblatt MATH identifier
1312.34054

#### Citation

Fonda, Alessandro; Garrione, Maurizio. Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane. Topol. Methods Nonlinear Anal. 42 (2013), no. 2, 293--325. https://projecteuclid.org/euclid.tmna/1461248981

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