迁移理论中一类具扰动的Chandrasekhar H-方程解的存在性定理*
Existence Theorems for a Class of Chandrasekhar H-Equation with Perturbation in Transport Theory
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摘要: 本文对迁移理论中一类具扰动的Chandrasekhar H-方程解(在C[0,1]中)存在性和逼近问题作了某些研究。本文结果改进和发展了引文[1~9]中的某些结果。Abstract: In this paper, the existence and approximation theorems of positive solutions in space C[0,1] for a class of Chandrasekhar H-equations with perturbation in transport theory ane proved. The results presented in this paper improve and extend some recent results in [1-9].
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[1] Chandrasekhar,S.,Radiative Transfer,Dover,New York(1960). [2] Legget,R.W.,On certain nonlinear integral equations,J.Math.Anal.Appl.,57(1977),462-468. [3] Stuart,C.A.,Existence theorems for a class of nonlinear integral,equations,Math.Z.,137(1974),49-66. [4] Hively,G.A.,On a class of nonlinear integral equations arising in transport theory,SIAM Math.Anal.,9,5(1978),787-792. [5] Cahlon,B.and M.Eskin,Existence theorems for an integral equation of the Chandrasekhar H-equation with perturbation,J.Math.Anal.Appl.,83(1981),159-171. [6] 刘清荣,在迁移理论中一类非线性积分方程的极大解和极小解,科学通报,1(1982),4-8. [7] 白锦东,迁移理论中一类非线性积分方程的唯二性,数学物理学报,4, 4 (1984),393-398. [8] Legget,R.W.,A new approach to the H-equation of Chandrasekhar,SIAM Math.Anal.,7,4(1976),542-550. [9] Busbridge,I.W.,On the H-function of Chandrasekhar,Quart.J.Math.,Oxford Ser,8 (1957),133-140. [10] Zhang Shi-sheng,Integral Equations, Chongqing Press(1986).(in Chinese) [11] Istratescu,V.I.,Fixed Point Theory.D.Reidel Publishing Company,Holland(1981). [12] Friedman,A.,Partial Differential Equations of Parabolic Type,Prentice-Hall,Englewood Cliffs,N.J.(1964).
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