On unbounded solutions for differential equations with mean curvature operator

Zuzana Došlá; Mauro Marini; Serena Matucci

Czechoslovak Mathematical Journal (2025)

  • Issue: 1, page 215-234
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Došlá, Zuzana, Marini, Mauro, and Matucci, Serena. "On unbounded solutions for differential equations with mean curvature operator." Czechoslovak Mathematical Journal (2025): 215-234. <http://eudml.org/doc/299904>.

@article{Došlá2025,
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.},
author = {Došlá, Zuzana, Marini, Mauro, Matucci, Serena},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear differential equation; curvatore operator; boundary value problem on the half line; fixed point theorem; unbounded solution},
language = {eng},
number = {1},
pages = {215-234},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On unbounded solutions for differential equations with mean curvature operator},
url = {http://eudml.org/doc/299904},
year = {2025},
}

TY - JOUR
AU - Došlá, Zuzana
AU - Marini, Mauro
AU - Matucci, Serena
TI - On unbounded solutions for differential equations with mean curvature operator
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 215
EP - 234
AB - 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.
LA - eng
KW - nonlinear differential equation; curvatore operator; boundary value problem on the half line; fixed point theorem; unbounded solution
UR - http://eudml.org/doc/299904
ER -

References

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