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Bounded Solutions of Some Second Order Nonlinear Differential Equations
Author(s) -
Mawhin Jean,
Ward James R.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006784
Subject(s) - bounded function , mathematics , nonlinear system , limiting , mathematical analysis , order (exchange) , mathematical proof , differential equation , type (biology) , real line , physics , geometry , mechanical engineering , ecology , finance , quantum mechanics , engineering , economics , biology
We prove Landesman–Lazer type existence conditions for the solutions bounded on the real line, together with their first derivatives, for some second order nonlinear differential equations of the form x ″+ cx ′+ f ( t , x )=0. The proofs use upper and lower solutions techniques together with some limiting arguments.