Interval criteria for oscillation of second-order differential equations with mixed nonlinearities. (English) Zbl 1141.34317

Sun, Yuan Gong; Meng, Fan Wei

Appl. Math. Comput. 198, No. 1, 375-381 (2008).

Summary: We establish interval criteria for oscillation of the second order forced ordinary differential equations with mixed nonlinearities:
\[ (p(t)x')'+q(t)x+\sum^n_{i=1}q_i(t)|x|^{\alpha_i}\text{sgn\,}x=e(t), \]
where \(p(t\)), \(q(t)\), \(q_i(t)\), \(e(t)\) are continuous functions defined on \([0,\infty)\), \(p(t)\) is positive and differentiable, \(\alpha_1 >\cdots >a_m > 1 > a_{m+1} >\cdots > a_n > 0\) \((n > m \geq 1)\). No restriction is imposed on the potentials \(q(t)\), \(q_i(t)\) and \(e(t)\) to be nonnegative.

MSC:

34C10

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Keywords:

interval criterion; second order; forced differential equation

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