Nonoscillatory Solutions to Forced Higher-order Nonlinear Neutral Dynamic Equations on Time Scales
نویسندگان
چکیده
By employing Kranoselskii’s fixed point theorem, we obtain sufficient conditions for the existence of nonoscillatory solutions of the forced higher-order nonlinear neutral dynamic equation [x(t) + p(t)x(τ(t))]∇ m + k ∑ i=1 pi(t)fi(x(τi(t))) = q(t) on a time scale, where pi(t), fi(t) and q(t) may be oscillatory. Then we establish sufficient and necessary conditions for the existence of nonoscillatory solutions to the equation [x(t) + p(t)x(τ(t))]∇ m + F (t, x(δ(t))) = q(t). Finally, we deal with dynamic equation [x(t) + p(t)x(τ(t))]∇ m−1∆ + k ∑ i=1 pi(t)fi(x(τi(t))) = q(t) with mixed ∇ and ∆ derivatives. In particular, some interesting examples are included to illustrate the versatility of our results.
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