孙经先.关于Hammerstein型非线性积分方程固有值的一点注记[J].数学研究及应用,1984,4(1):51~53
关于Hammerstein型非线性积分方程固有值的一点注记
A Note on Eigenvalues of Hammerstein Nonlinear Integral Equations
投稿时间:1981-10-20  
DOI:10.3770/j.issn:1000-341X.1984.01.011
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孙经先 山东大学数学系 
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英文摘要:
      Let Aφ(x)=∫GK(x,y)f(y,φ(y))dy, where G is a bounded closed domain in Euclidean space, K(x,y) is continuous on G×G, f(x,u) is continuous on G×R, and f(x,0)≡0. Set Gx={x|x∈G,K(x,y)≠0},Gy={y|y∈G,K(x,y)≠0},G1=Gx∩Gy≠φ.Let K1(x,y) be the restriction of K(x,y) on G1×G1,f1(x,u)be the restriction of f(x, u) on G1× R, and A1φ=∫G1K1(x,y)f1(y,φ1(y))dy, The main result of this paper is Theorem λ≠0 is an eigenvalue of A, if and only if λ is an eigenvalue of A1.
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