TY - JOUR
T1 - Applications of generalized trigonometric functions with two parameters
AU - Kobayashi, Hiroyuki
AU - Takeuchi, Shingo
N1 - Funding Information:
2000 Mathematics Subject Classification. Primary: 33B10, 34B10. Key words and phrases. Generalized trigonometric functions, p-Laplacian, Gaussian hyperge- ometric functions, Wallis-type formulas. The work of S. Takeuchi was supported by JSPS KAKENHI Grant Number 17K05336. ∗ Corresponding author.
Publisher Copyright:
© 2018 American Institute of Mathematical Sciences. All rights reserved.
PY - 2019/5
Y1 - 2019/5
N2 - Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the p-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the p-Laplacian. However, few applications to differential equations unrelated to the p-Laplacian are known. We will apply GTFs with two parameters to nonlinear nonlocal boundary value problems without p-Laplacian. Moreover, we will give integral formulas for the functions, e.g. Wallis-type formulas, and apply the formulas to the lemniscate function and the lemniscate constant.
AB - Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the p-Laplacian, which is known as a typical nonlinear differential operator, and there are a lot of works on GTFs concerning the p-Laplacian. However, few applications to differential equations unrelated to the p-Laplacian are known. We will apply GTFs with two parameters to nonlinear nonlocal boundary value problems without p-Laplacian. Moreover, we will give integral formulas for the functions, e.g. Wallis-type formulas, and apply the formulas to the lemniscate function and the lemniscate constant.
KW - Gaussian hypergeometric functions
KW - Generalized trigonometric functions
KW - P-Laplacian
KW - Wallis-type formulas
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U2 - 10.3934/cpaa.2019072
DO - 10.3934/cpaa.2019072
M3 - Article
AN - SCOPUS:85056482954
SN - 1534-0392
VL - 18
SP - 1509
EP - 1521
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 3
ER -