A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type

Soohyun Bae

Archivum Mathematicum (2023)

  • Issue: 2, page 155-162
  • ISSN: 0044-8753

Abstract

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We consider the quasilinear equation Δ p u + K ( | x | ) u q = 0 , and present the proof of the local existence of positive radial solutions near 0 under suitable conditions on K . Moreover, we provide a priori estimates of positive radial solutions near ∞ when r - ℓ K ( r ) for ℓ ≥ - p is bounded near ∞ .

How to cite

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Bae, Soohyun. "A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type." Archivum Mathematicum (2023): 155-162. <http://eudml.org/doc/298973>.

@article{Bae2023,
abstract = {We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates of positive radial solutions near $\infty $ when $r^\{-\ell \}K(r)$ for $\ell \ge -p$ is bounded near $\infty $.},
author = {Bae, Soohyun},
journal = {Archivum Mathematicum},
keywords = {quasilinear equation; positive solution; a priori bound},
language = {eng},
number = {2},
pages = {155-162},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type},
url = {http://eudml.org/doc/298973},
year = {2023},
}

TY - JOUR
AU - Bae, Soohyun
TI - A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 2
SP - 155
EP - 162
AB - We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates of positive radial solutions near $\infty $ when $r^{-\ell }K(r)$ for $\ell \ge -p$ is bounded near $\infty $.
LA - eng
KW - quasilinear equation; positive solution; a priori bound
UR - http://eudml.org/doc/298973
ER -

References

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  1. Bidaut-Véron, M.-F., Pohozaev, S., 10.1007/BF02788105, J. Anal. Math. 84 (2001), 1–49. (2001) MR1849197DOI10.1007/BF02788105
  2. Kawano, N., Ni, W.-M., Yotsutani, S., 10.2969/jmsj/04230541, J. Math. Soc. Japan 42 (1990), 541–564. (1990) DOI10.2969/jmsj/04230541
  3. Kawano, N., Yanagida, E., Yotsutani, S., Structure theorems for positive radial solutions to div ( | D u | m - 2 D u ) + K ( | x | ) u q = 0 in 𝐑 n , J. Math. Soc. Japan 45 (1993), 719–742. (1993) 
  4. Li, Y., Ni, W.-M., On conformal scalar curvature equation in 𝐑 n , Duke Math. J. 57 (1988), 895–924. (1988) 
  5. Ni, W.-M., Serrin, J., Existence and non-existence theorems for ground states of quasilinear partial differential equations: The anomalous case, Atti Convegni Lincei 77 (1986), 231–257. (1986) 
  6. Serrin, J., Zou, H., 10.1007/BF02392645, Acta Math. 189 (2002), 79–142. (2002) MR1946918DOI10.1007/BF02392645

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