Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian
Asymptotic properties for solutions of differential equations with singular p(t)-Laplacian
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奇异 p(t)-拉普拉斯微分方程解的渐近性质
DOI：
10.1007/s00605-023-01835-0
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发表时间：
2023
影响因子：
0.9
通讯作者：
Fujimoto Kodai
中科院分区：
文献类型：
--
作者：
Dosla Zuzana;Fujimoto Kodai
本文讨论了一类非线性微分方程解的非振动性，包括：[12pt]{minimum}\usepackage{amsath}\usepackage{wa ysym}\usepackage{amsfonts}\usepackage{amsbsy}\usepackage{mathsfs}\usepackage{upgreek}\setlong{\oddsidemargin}{-69pt}\Begin{Document}$\Left(a(T)|x{^\Prime}|^{p(T)-2X{^\Prime}\right){^\Prime}+b(T)|x|^{\lambda-2}x=0$$\end{DOCUMENT}涉及“奇异”p(T)-拉普拉斯。给出了常规情况下不存在的极值解存在的充分条件。此外，我们还证明了极值解和弱增加解的共存。文中给出了一些例子来说明我们的结果。
This paper deals with the nonoscillatory solutions of the nonlinear differential equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( a(t)|x{^\prime }|^{p(t)-2}x{^\prime }\right) {^\prime }+b(t)|x|^{\lambda -2}x=0$$\end{document} 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.