We study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity
Dalbono F, Rebelo C (2009). Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 52(3), 569-581 [10.1017/S0013091506000897].
Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2
DALBONO, Francesca;
2009-01-01
Abstract
We study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity
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