Czechoslovak Mathematical Journal, first online, pp. 1-20
On unbounded solutions for differential equations with mean curvature operator
Zuzana Došlá, Mauro Marini, Serena Matucci
Received March 13, 2023. Published online September 6, 2023. OPEN ACCESS
Abstract: We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived.
Keywords: nonlinear differential equation; curvatore operator; boundary value problem on the half line; fixed point theorem; unbounded solution
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Affiliations: Zuzana Došlá (corresponding author), Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic e-mail: dosla@math.muni.cz; Mauro Marini, Serena Matucci, Department of Mathematics and Computer Science `Ulisse Dini', University of Florence, Via di S. Marta 3, 50139 Florence, Italy, e-mail: mauro.marini@unifi.it, serena.matucci@unifi.it
