MATHEMATICA BOHEMICA, Vol. 127, No. 2, pp. 181-195 (2002)

Qualitative theory of half-linear second order differential equations

Ondrej Dosly

Ondrej Dosly, Mathematical Institute, Czech Academy of Sciences, Zizkova 22, CZ-616 62 Brno, e-mail:

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

Keywords: half-linear equation, Picone's identity, scalar $p$-Laplacian, variational method, Riccati technique, principal solution

Classification (MSC2000): 34C10

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