Comparison results and existence of bounded solutions to strongly nonlinear second order differential equations
Keywords
Nonlinear ordinary differential operator, bounded solutions, non-compact interval, upper and lower solutions, comparison resultAbstract
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.Downloads
Published
2009-09-01
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1.
MARCELLI, Cristina and PAPALINI, Francesca. Comparison results and existence of bounded solutions to strongly nonlinear second order differential equations. Topological Methods in Nonlinear Analysis. Online. 1 September 2009. Vol. 36, no. 1, pp. 91 - 110. [Accessed 28 March 2024].
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