We consider a class of superlinear conservative ordinary differential systems in Newtonian form: -Ü = ∇E(t,U), U(t) ∈ ℝn with t ∈ [A, B]. We prove the existence of infinitely many solutions to the Dirichlet boundary value problem. Such solutions are characterized by the number of zeroes of each component. Our argument is based upon an extension of the Nehari variational method
Terracini, S., Verzini, G. (2001). Solutions of prescribed number of zeroes to a class of superlinear ODE's systems. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 8(3), 323-341 [10.1007/PL00001451].
Solutions of prescribed number of zeroes to a class of superlinear ODE's systems
TERRACINI, SUSANNA;
2001
Abstract
We consider a class of superlinear conservative ordinary differential systems in Newtonian form: -Ü = ∇E(t,U), U(t) ∈ ℝn with t ∈ [A, B]. We prove the existence of infinitely many solutions to the Dirichlet boundary value problem. Such solutions are characterized by the number of zeroes of each component. Our argument is based upon an extension of the Nehari variational method
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