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S. T. WU


In this paper the existence of the solution for elliptic integro-differential systems are discussed. Those systems are motivated by certain physical processes such as in epidemics, predator-prey dynamics and the others. We extend the method of mixed monotony to second order elliptic partial integro-differential equations. By assuming the existence of a satellite $f$ of the give function $\Phi$, we prove the existence of solutions by using fixed point theory. Moreover, we provide the modified method of mixed monotony to construct two monotone sequences which converge uniformly to the solution. We also give sufficient conditions for the existence of $f$ and obtain the construction of upper and lower solutions in some applications.

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TSAI, L.-Y., & WU, S. T. (1995). EXISTENCE OF SOLUTIONS FOR ELLIPTIC INTEGRO-DIFFERENTIAL SYSTEMS. Tamkang Journal of Mathematics, 25(1), 61–70. https://doi.org/10.5556/j.tkjm.25.1994.4426


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