This paper considers a class of Schrödinger elliptic system involving a nonlinear operator. Firstly, under the simple condition on and ', we prove the existence of the entire positive bounded radial solutions. Secondly, by using the iterative technique and the method of contradiction, we prove the existence and nonexistence of the entire positive blow-up radial solutions. Our results extend the previous existence and nonexistence results for both the single equation and systems. In the end, we give two examples to illustrate our results.
In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results.
In this paper, the rotor system with nonlinear bearing force and base excitation load was modeled based on finite element method, and its response characteristic under the excitation of base load was studied. The results show that the response of the rotor is the superposition of the basic impulse response and the unbalanced response. The pulse excitation energy can be dispersed while the rotation speed and pulse frequency are close to each other. When the phase difference of unbalanced excitation is 180°, the response amplitude of rotor bearing system was the smallest. The correctness of the rotor bearing system model was verified by experiments.
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