In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impuls...The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impulsive integro\|differential equations in Banach spaces.Finally,the existence theorem on the maximal and minimal solutions is obtained.展开更多
We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim dist...We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.展开更多
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
文摘The comparison principle is first established,and then the lower and upper solution method and the monotone iterative technique are employed to the study of terminal value problems for the first order nonlinear impulsive integro\|differential equations in Banach spaces.Finally,the existence theorem on the maximal and minimal solutions is obtained.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11171179）.
文摘We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.
