Qualitative theory of half-linear second order differential equations

Ondřej Došlý

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 181-195
  • ISSN: 0862-7959

Abstract

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Some recent results concerning properties of solutions of the half-linear second order differential equation ( r ( t ) Φ ( x ' ) ) ' + c ( t ) Φ ( x ) = 0 , Φ ( x ) : = | x | p - 2 x , p > 1 , ( * ) are presented. A particular attention is paid to the oscillation theory of ( * ) . Related problems are also discussed.

How to cite

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Došlý, Ondřej. "Qualitative theory of half-linear second order differential equations." Mathematica Bohemica 127.2 (2002): 181-195. <http://eudml.org/doc/249043>.

@article{Došlý2002,
abstract = {Some recent results concerning properties of solutions of the half-linear second order differential equation \[ (r(t)\Phi (x^\{\prime \}))^\{\prime \}+c(t)\Phi (x)=0,\quad \Phi (x):=|x|^\{p-2\}x,\quad p>1, \qquad \mathrm \{\{(*)\}\}\] are presented. A particular attention is paid to the oscillation theory of $(*)$. Related problems are also discussed.},
author = {Došlý, Ondřej},
journal = {Mathematica Bohemica},
keywords = {half-linear equation; Picone’s identity; scalar $p$-Laplacian; variational method; Riccati technique; principal solution; half-linear equation; Picone's identity; scalar -Laplacian; variational method; Riccati technique; principal solution},
language = {eng},
number = {2},
pages = {181-195},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Qualitative theory of half-linear second order differential equations},
url = {http://eudml.org/doc/249043},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Došlý, Ondřej
TI - Qualitative theory of half-linear second order differential equations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 181
EP - 195
AB - Some recent results concerning properties of solutions of the half-linear second order differential equation \[ (r(t)\Phi (x^{\prime }))^{\prime }+c(t)\Phi (x)=0,\quad \Phi (x):=|x|^{p-2}x,\quad p>1, \qquad \mathrm {{(*)}}\] are presented. A particular attention is paid to the oscillation theory of $(*)$. Related problems are also discussed.
LA - eng
KW - half-linear equation; Picone’s identity; scalar $p$-Laplacian; variational method; Riccati technique; principal solution; half-linear equation; Picone's identity; scalar -Laplacian; variational method; Riccati technique; principal solution
UR - http://eudml.org/doc/249043
ER -

References

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