The method of upper and lower solutions for diffraction problems of quasilinear elliptic reaction-diffusion systems |
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Authors: | Qi-Jian Tan Zhong-Jian Leng |
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Institution: | a Department of Mathematics, Sichuan College of Education, Chengdu 610041, China b College of Mathematics, Sichuan University, Chengdu 610064, China |
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Abstract: | The aim of this paper is to show the existence of solutions of the n-dimensional diffraction problem for weakly coupled quasilinear elliptic reaction-diffusion system. The coefficients of the equations under consideration are allowed to be discontinuous. We extend the method of upper and lower solutions for reaction-diffusion equations with continuous coefficients to the elliptic diffraction problem. An application of these results is given to the steady-state problem of Lotka-Volterra cooperation model with two cooperating species. |
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Keywords: | Diffraction problem Quasilinear elliptic systems Reaction-diffusion Upper and lower solutions |
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