Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian

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Authors

DOŠLÁ Zuzana FUJIMOTO Kodai

Year of publication 2023
Type Article in Periodical
Magazine / Source Monatshefte für Mathematik
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1007/s00605-023-01835-0
Doi http://dx.doi.org/10.1007/s00605-023-01835-0
Keywords Asymptotic behavior; Nonoscillatory solutions; Extremal solutions; Weakly increasing solutions; p(t)-Laplacian; Half-linear differential equations
Description This paper deals with the nonoscillatory solutions of the nonlinear differential equation (a(t)|x'|(p(t)-2)x')' +b(t)|x|(?-2)x = 0 involving "singular" p(t)-Laplacian. Sufficient conditions are given for the existence of extremal solutions, which do not exist in the conventional cases. In addition, we prove the coexistence of extremal solutions and weakly increasing solutions. Some examples are given to illustrate our results.
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