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Zbl 1101.34019
Došlý, Ondřej
Pseudoconjugacy criteria for half-linear second order differential equations. (English)
[J] Miskolc Math. Notes 6, No. 2, 161-172 (2005). ISSN 1787-2405; ISSN 1787-2413/e

Summary: Using the variational principle, we present sufficient conditions for the existence of a pair of pseudoconjugate points in an interval $I\subseteq \Bbb{R}$ relative to the half-linear second-order differential equation $$\left(r(t)\Phi(x')\right)'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2}x,\ p>1. \leqno{(*)}$$ The endpoints of the interval $I$ are allowed to be singular (in particular, the case $I=\Bbb{R}$ is possible) and an important role is played by the principal solution of (*) and of its reciprocal equation.

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: half-linear differential equation; pseudoconjugate points; pseudoconjugacy criterion; variational method; principal solution; reciprocal equation; coprincipal solution

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