Oscillation criteria for nonlinear differential equations with $p(t)$-Laplacian
Recently there has been an increasing interest in studying $p(t)$-Laplacian equations, an example of which is given in the following form (|u'(t)|^{p(t)-2}u'(t))'+c(t)|u(t)|^{q(t)-2}u(t)= 0, \quad t>0. In particular, the first study of sufficient conditions for oscillator...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2016-04-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/141/1/mb141_1_5.pdf |
| Summary: | Recently there has been an increasing interest in studying $p(t)$-Laplacian equations, an example of which is given in the following form
(|u'(t)|^{p(t)-2}u'(t))'+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). |
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| ISSN: | 0862-7959 2464-7136 |