Year: 2025
Type: article
Abstract: This paper investigates the asymptotic behavior of increasing solutions to subhomogeneous differential equations involving the p ( t )-Laplacian operator. Specifically, we consider the quasilinear equation $$(a(t)|y'|^{p(t)}\mathop {\textrm{sgn}}\nolimits {y'})'=b(t)|y|^{q(t)}L_G(|y|)\mathop {\textrm{sgn}}\nolimits {y}$$ ( a ( t ) | y ′ | p ( t ) sgn y ′ ) ′ = b ( t ) | y | q ( t ) L G ( | y | ) sgn y where p ( t ) and q ( t ) are variable exponents and $$L_G$$ L G is a slowly varying perturbation. Our focus is on regularly varying solutions under the subhomogeneity condition $$p(t)>q(t)$$ p ( t ) > q ( t ) for large t . We show that all increasing solutions are regularly varying, derive asymptotic formulas for these solutions, and demonstrate their examples. This work contributes to the understanding of nonoscillatory solutions and shows how regular variation can be useful in studying differential equations involving variable exponents.
Authors: Kōdai Fujimoto, Pavel Řehák
Institutions: Shimane University, Brno University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: Vysoké Učení Technické v Brně
OpenAlex ID: W4416025811