Decaying positive solutions of some quasilinear differential equations

Tadie

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 39-47
  • ISSN: 0010-2628

Abstract

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The existence of decaying positive solutions in ℝ + of the equations ( E λ ) and ( E λ 1 ) displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. t 1 - p F ( r , t U , t | U ' | ) ↘ 0 as t ↗ ∞ ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.

How to cite

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Tadie. "Decaying positive solutions of some quasilinear differential equations." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 39-47. <http://eudml.org/doc/248235>.

@article{Tadie1998,
abstract = {The existence of decaying positive solutions in $\{\mathbb \{R\}\}_+$ of the equations $(E_\lambda )$ and $(E_\lambda ^1)$ displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. $t^\{1-p\} F(r,tU,t|U^\{\prime \}|) \searrow 0$ as $t \nearrow \infty $), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.},
author = {Tadie},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasilinear elliptic; integral operators; fixed points theory; -Laplacian; radial solution; decaying positive solution; super-sub-solution method},
language = {eng},
number = {1},
pages = {39-47},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Decaying positive solutions of some quasilinear differential equations},
url = {http://eudml.org/doc/248235},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Tadie
TI - Decaying positive solutions of some quasilinear differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 39
EP - 47
AB - The existence of decaying positive solutions in ${\mathbb {R}}_+$ of the equations $(E_\lambda )$ and $(E_\lambda ^1)$ displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. $t^{1-p} F(r,tU,t|U^{\prime }|) \searrow 0$ as $t \nearrow \infty $), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.
LA - eng
KW - quasilinear elliptic; integral operators; fixed points theory; -Laplacian; radial solution; decaying positive solution; super-sub-solution method
UR - http://eudml.org/doc/248235
ER -

References

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  2. Istratescu V.I., Fixed Point Theory, Math. and its Appl., Reidel Publ. (1981). (1981) Zbl0465.47035MR0620639
  3. Kawano N., Yanagida E., Yotsutani S., Structure theorems for positive radial solutions to d i v ( | D u | m - 2 D u ) + K ( | x | ) u q = 0 in ℝ n , J. Math. Soc. Japan 45 no. 4 (1993), 719-742. (1993) Zbl0803.35040MR1239344
  4. Kusano T., Swanson C.A., Radial entire solutions of a class of quasilinear elliptic equations, J.D.E. 83 (1990), 379-399. (1990) Zbl0703.35060MR1033194
  5. Tadie, Weak and classical positive solutions of some elliptic equations in ℝ n , n ≥ 3 : radially symmetric cases, Quart. J. Oxford 45 (1994), 397-406. (1994) MR1295583
  6. Tadie, Subhomogeneous and singular quasilinear Emden-type ODE, to appear. Zbl1058.34505
  7. Yasuhiro F., Kusano T., Akio O., Symmetric positive entire solutions of second order quasilinear degenerate elliptic equations, Arch. Rat. Mech. Anal. 127 (1994), 231-254. (1994) Zbl0807.35035MR1288603
  8. Yin Xi Huang, Decaying positive entire solutions of the p-Laplacian, Czech. Math. J. 45 no. 120 (1995), 205-220. (1995) MR1331458

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