## Limit circle type results for sublinear equations.(English)Zbl 0535.34024

The author considers forced second order nonlinear equations of the type $$(a(t)x')'+q(t)f(x)=r(t)$$ and calls them of nonlinear limit circle type if every solution x(t) has $$\int^{\infty}_{t_ 0}x(u)f(x(u))du<\infty$$ and of nonlinear limit point type otherwise (this definition generalizes H. Weyl’s [Math. Ann. 68, 220-269 (1910)] classification of second order linear differential equations $$(a(t)x')'+q(t)x=0)$$. The author considers the sublinear case $$f(x)=x^{\gamma}$$, $$0<\gamma \leq 1$$. Necessary and sufficient conditions are found that such a forced or unforced $$(r=0)$$ equation is of nonlinear limit circle type and also sufficient conditions that it is of nonlinear limit point type.
Reviewer: M.Boudourides

### MSC:

 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34A30 Linear ordinary differential equations and systems
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