EXISTENCE OF SOLUTIONS FOR ELLIPTIC INTEGRO-DIFFERENTIAL SYSTEMS

Article Sidebar

PDF
Published: Mar 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.25.1994.4426
Keywords:
Satellite epsilon-upper(epsilon-lower) solutions upper(lower) solutions

Main Article Content

LONG-YI TSAI
Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan, R. O. C. 11623.
S. T. WU
Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan, R. O. C. 11623.

Abstract




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.




Article Details

How to Cite
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
Issue
Vol. 25 No. 1 (1994)
Section
Papers
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

D. Gilbarg and N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order", Springer Verlag, 1983.

M. Khavanin, "The method of mixed monotony and second order integro-differential system", Appl. Anal. 28 (1988), 199-206.

M. Khavanin and V. Lakshmikantham, "The method of mixed monotony and second order boundary value problems", JMAA, 120 (1986), 737-744.

P. de. Mottoni, E. Orlandi and A. Tesei, "Asymptotic behavior for a system describing epidemics with migration and spatial spread of infection", Nonlinear Analysis, TMA, 3 (1979), 663-675.

V. I. Opoitsev, "Generalization of the theory of monotone and concave operators", Tr. Mosk. Mathem, 36 (1978), 237-273.

C.V. Pao, "On nonlinear reaction-diffusion systems", JMAA, 87 (1982), 165-198.

V. P. Politjukov, "On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations", Math. USSR, Sbornik, 35 (1979), 499-507.

M. H. Protter and H. F. Weinberger, "Maximum Principles in Differential Equations", Prentice-Hall, Englewood, Cliffs, N.J., 1967.

R. Redlinger, "Lower and upper solution for strongly coupled systems of reaction diffusion equationss, Proceeding of inte1 1ational conference on theory and application of differential equations", Ohio Univ., (1988), 327-332.

L.Y. Tsai, "On the solvability of nonlinear integro-differential operators", Chinese J. Math., (1983), 75-84.