Positive solutions with a complex behavior for superlinear indefinite ODEs on the real line
| Autor: | Vivina Barutello, Gianmaria Verzini, Alberto Boscaggin |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Pure mathematics
Applied Mathematics Scalar (mathematics) Ode Natural constraints Nehari method Periodic and subharmonic solutions Singularly perturbed problems Analysis Arbitrarily large Nonlinear system 34B18 34C25 34C28 37J45 Mathematics - Classical Analysis and ODEs Bounded function Classical Analysis and ODEs (math.CA) FOS: Mathematics Real line Mathematics |
| Popis: | We show the existence of infinitely many positive solutions, defined on the real line, for the nonlinear scalar ODE \[ \ddot u + (a^+(t) - ��a^-(t)) u^3 = 0, \] where $a$ is a periodic, sign-changing function, and the parameter $��>0$ is large. Such solutions are characterized by the fact of being either small or large in each interval of positivity of $a$. In this way, we find periodic solutions, having minimal period arbitrarily large, and bounded non-periodic solutions, exhibiting a complex behavior. The proof is variational, exploiting suitable natural constraints of Nehari type. 35 pages |
| Databáze: | OpenAIRE |
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