We study the existence of positive solutions on the positive half-line for a nonlinear second order differential equation satisfying Dirichlet type conditions, say x(0) = 0, lim x(t) = 0 as t goes to infinity. The weight function is allowed to change sign and the nonlinearity is assumed to be asymptotically linear in a neighborhood of zero and infnity. Our results cover also the cases in which the weight is a periodic function for large t or it is unbounded from below.
A Dirichlet problem on the half-line for nonlinear equations with indefinite weight / Dosla, Zuzana; Marini, Mauro; Serena, Matucci. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 1618-1891. - STAMPA. - 196:(2017), pp. 51-64. [10.1007/s10231-016-0562-y]
A Dirichlet problem on the half-line for nonlinear equations with indefinite weight
MARINI, MAURO;MATUCCI, SERENA
2017
Abstract
We study the existence of positive solutions on the positive half-line for a nonlinear second order differential equation satisfying Dirichlet type conditions, say x(0) = 0, lim x(t) = 0 as t goes to infinity. The weight function is allowed to change sign and the nonlinearity is assumed to be asymptotically linear in a neighborhood of zero and infnity. Our results cover also the cases in which the weight is a periodic function for large t or it is unbounded from below.
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