English

Abstract

Recently there has been an increasing interest in studying $p(t)$-Laplacian equations, an example of which is given in the following form $$ (|u'(t)|^{p(t)-2}u'(t))'+c(t)|u(t)|^{q(t)-2}u(t)= 0, \quad t>0. $$ 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).