On the behavior of solutions of sublinear second order differential equations

Teufel, Hugo

doi:10.1090/S0002-9939-1972-0294773-1

On the behavior of solutions of sublinear second order differential equations
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Proc. Amer. Math. Soc. 32 (1972), 445-451 Request permission

Abstract:

The equations in question generalize \[ x'' + a(t)|x{|^\gamma }\operatorname {sgn} x = 0,\quad 0 < \gamma < 1,\quad a(t) \geqq 0.\]. A comparison theorem and a uniqueness theorem for initial value problems are proved. Boundary value problems are studied. Oscillation is discussed via comparison.

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