Double resonance in Sturm-Liouville planar boundary value problems
Copyright policy )Double resonance in Sturm-Liouville planar boundary value problems
We provide some existence results for Sturm-Liouville boundary value problems associated with the planar differential system $Jz' = g(t, z) + r(t, z)$ where g is suitably controlled by the gradient of two positively homogeneous functions of degree 2 and r is bounded. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman-Lazer type of conditions. Applications to scalar second order differential equations are given.
- University of Trieste Italy
- Marche Polytechnic University Italy
Shooting method, shooting method, Dynamical Systems (math.DS), Positively homogeneous planar system, Sturm-Liouville theory, Double resonance, FOS: Mathematics, Landesman-Lazer condition, Sturm{Liouville boundary value problems, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, Sturm-Liouville boundary value problems, Landesman-Lazer conditions, Dirichlet problem; Double resonance; Landesman-Lazer conditions; Positively homogeneous planar systems; Shooting method; Sturm{Liouville boundary value problems, double resonance, positively homogeneous planar systems, Dirichlet problem
Shooting method, shooting method, Dynamical Systems (math.DS), Positively homogeneous planar system, Sturm-Liouville theory, Double resonance, FOS: Mathematics, Landesman-Lazer condition, Sturm{Liouville boundary value problems, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, Sturm-Liouville boundary value problems, Landesman-Lazer conditions, Dirichlet problem; Double resonance; Landesman-Lazer conditions; Positively homogeneous planar systems; Shooting method; Sturm{Liouville boundary value problems, double resonance, positively homogeneous planar systems, Dirichlet problem
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