Oscillation criteria for nonlinear differential equations with $p\left(t\right)$-Laplacian

Shoukaku, Yutaka. "Oscillation criteria for nonlinear differential equations with $p(t)$-Laplacian." Mathematica Bohemica 141.1 (2016): 71-81. <http://eudml.org/doc/276815>.

@article{Shoukaku2016,
abstract = {Recently there has been an increasing interest in studying $p(t)$-Laplacian equations, an example of which is given in the following form \[ (|u^\{\prime \}(t)|^\{p(t)-2\}u^\{\prime \}(t))^\{\prime \}+c(t)|u(t)|^\{q(t)-2\}u(t)= 0, \quad t>0. \] In particular, the first study of sufficient conditions for oscillatory solution of $p(t)$-Laplacian equations was made by Zhang (2007), but to our knowledge, there has not been a paper which gives the oscillatory conditions by utilizing Riccati inequality. Therefore, we establish sufficient conditions for oscillatory solution of nonlinear differential equations with $p(t)$-Laplacian via Riccati method. The results obtained are new and rare, except for a work of Zhang (2007). We present more detailed results than Zhang (2007).},
author = {Shoukaku, Yutaka},
journal = {Mathematica Bohemica},
keywords = {$p(t)$-Laplacian; oscillation theory; Riccati inequality},
language = {eng},
number = {1},
pages = {71-81},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation criteria for nonlinear differential equations with $p(t)$-Laplacian},
url = {http://eudml.org/doc/276815},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Shoukaku, Yutaka
TI - Oscillation criteria for nonlinear differential equations with $p(t)$-Laplacian
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 1
SP - 71
EP - 81
AB - Recently there has been an increasing interest in studying $p(t)$-Laplacian equations, an example of which is given in the following form \[ (|u^{\prime }(t)|^{p(t)-2}u^{\prime }(t))^{\prime }+c(t)|u(t)|^{q(t)-2}u(t)= 0, \quad t>0. \] In particular, the first study of sufficient conditions for oscillatory solution of $p(t)$-Laplacian equations was made by Zhang (2007), but to our knowledge, there has not been a paper which gives the oscillatory conditions by utilizing Riccati inequality. Therefore, we establish sufficient conditions for oscillatory solution of nonlinear differential equations with $p(t)$-Laplacian via Riccati method. The results obtained are new and rare, except for a work of Zhang (2007). We present more detailed results than Zhang (2007).
LA - eng
KW - $p(t)$-Laplacian; oscillation theory; Riccati inequality
UR - http://eudml.org/doc/276815
ER -