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Pseudoconjugacy criteria for half-linear second order differential equations. (English) Zbl 1101.34019
Summary: Using the variational principle, we present sufficient conditions for the existence of a pair of pseudoconjugate points in an interval $$I\subseteq \mathbb{R}$$ relative to the half-linear second-order differential equation
$\left(r(t)\Phi(x')\right)'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2}x,\;p>1. {(*)}$
The endpoints of the interval $$I$$ are allowed to be singular (in particular, the case $$I=\mathbb{R}$$ is possible) and an important role is played by the principal solution of (*) and of its reciprocal equation.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations