Comparison results and existence of bounded solutions to strongly nonlinear second order differential equations
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Nonlinear ordinary differential operator, bounded solutions, non-compact interval, upper and lower solutions, comparison resultAbstrakt
We investigate the existence of bounded solutions on the whole real line of the following strongly non-linear non-autonomous differential equation $$ (a(x(t))x'(t))'= f(t,x(t),x'(t)) \quad \text{a.e } t\in \mathbb R \tag \text{\rm E} $$ where $a(x)$ is a generic continuous positive function, $f$ is a Carathéodory right-hand side. We get existence results by combining the upper and lower-solutions method to fixed-point techniques. We also provide operative comparison criteria ensuring the well-ordering of pairs of upper and lower-solutions.Pobrania
Opublikowane
2009-09-01
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1.
MARCELLI, Cristina & PAPALINI, Francesca. Comparison results and existence of bounded solutions to strongly nonlinear second order differential equations. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 2009, T. 36, nr 1, s. 91–110. [udostępniono 17.7.2024].
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