论文信息 - Constant‐sign solutions for singular systems of Fredholm integral equations

Constant‐sign solutions for singular systems of Fredholm integral equations

We consider the system of Fredholm integral equations u i (t)= ∫ T 0 g i (t,s)[H i (s, u 1 (s), u 2 (s),...,u n (s))+K i (s, u 1 (s), u 2 (s),...,u n (s))]ds, t∈[0, T], 1≤i≤n where T>0 is fixed and the nonlinearities H i (t, u 1 , u 2 ,..., u n ) can be singular at t=0 and u j =0 where j ∈{1, 2,..., n}. Criteria are offered for the existence of constant-sign solutions, i.e. θ i u i (t)≥0 for t∈[0, 1] and 1 ≤i≤n, where θ i ∈{1, ―1} is fixed. We also include an example to illustrate the usefulness of the results obtained.

[1] Ravi P. Agarwal,et al. Constant-Sign Solutions for Systems of Fredholm and Volterra Integral Equations: The Singular Case , 2008 .

[2] Wenjie Gao,et al. Singular nonlinear boundary value problems arising in boundary layer theory , 1999 .

[3] Ravi P. Agarwal,et al. Constant-Sign Solutions of a System of Fredholm Integral Equations , 2004 .

[4] Ravi P. Agarwal,et al. Nonlinear integral equations singular in the dependent variable , 2007, Appl. Math. Lett..

[5] Ravi P. Agarwal,et al. Constant-sign solutions of a system of integral equations: The semipositone and singular case , 2005 .

[6] Ravi P. Agarwal,et al. Constant-Sign Solutions of a System of Integral Equations with Integrable Singularities , 2007 .

[7] Ravi P. Agarwal,et al. Eigenvalues of a system of Fredholm integral equations , 2004 .

[8] Ravi P. Agarwal,et al. Opial's and wirtinger's type discrete inequalities in two independent variables , 1992 .

[9] Samuel Karlin,et al. On a Theorem of P. Nowosad , 1967 .

[10] D. O’Regan,et al. Positive Solutions of Singular Integral Equations , 2000 .

[11] P. Nowosad,et al. On the integral equation κf = 1f arising in a problem in communication , 1966 .

[12] P. Bushell,et al. On a class of Volterra and Fredholm non-linear integral equations , 1976, Mathematical Proceedings of the Cambridge Philosophical Society.