Open AccessEXISTENCE OF SOLUTIONS FOR ELLIPTIC INTEGRO-DIFFERENTIAL SYSTEMS
Author(s) -
Long-Yi Tsai,
Shuonan Wu
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.25.1994.4426
Subject(s) - mathematics , monotone polygon , order (exchange) , differential equation , function (biology) , partial differential equation , elliptic partial differential equation , mathematical analysis , pure mathematics , geometry , finance , economics , biology , evolutionary biology
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.