Access the full text.
Sign up today, get DeepDyve free for 14 days.
C. Corduneanu (1973)
Integral Equations and Stability of Feedback SystemsJournal of Dynamic Systems Measurement and Control-transactions of The Asme, 97
G. Bonanno (1995)
An existence theorem of positive solutions to a singular nonlinear boundary value problemComment. Math. Univ. Carol., 36
R. Agarwal, D. O’Regan, P. Wong (1998)
Positive Solutions of Differential, Difference and Integral Equations
D. O’Regan, M. Meehan (1998)
Existence Theory for Nonlinear Integral and Integrodifferential Equations
R. Agarwal, D. O’Regan, P. Wong (2007)
Constant-Sign Solutions of a System of Integral Equations with Integrable SingularitiesJournal of Integral Equations and Applications, 19
R. Agarwal, D. O’Regan, P. Wong (2004)
Eigenvalues of a system of Fredholm integral equationsMathematical and Computer Modelling, 39
P. Bushell, W. Okrasinski (1990)
Nonlinear Volterra Integral Equations with Convolution KernelJournal of The London Mathematical Society-second Series
W. Jones, W. Thron (1982)
Encyclopedia of Mathematics and its Applications.Mathematics of Computation, 39
R. Agarwal, D. O’Regan, C. Tisdell, P. Wong (2007)
Constant-sign solutions of a system of Volterra integral equationsComput. Math. Appl., 54
R. Agarwal, D. O’Regan, P. Wong (2005)
Constant-sign solutions of a system of integral equations: The semipositone and singular caseAsymptotic Analysis, 43
P. Bushell, W. Okrasinski (1989)
Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernelMathematical Proceedings of the Cambridge Philosophical Society, 106
S. Karlin, L. Nirenberg (1967)
On a Theorem of P. NowosadJournal of Mathematical Analysis and Applications, 17
M. Meehan, D. O’Regan (2000)
A note on singular Volterra functional-differential equationsMath. Proc. R. Ir. Acad., 100A
G. Gripenberg (1981)
Unique solutions of some Voltera integral equations.Mathematica Scandinavica, 48
M. Meehan, D. O’Regan (2000)
Positive Solutions of Singular Integral EquationsJournal of Integral Equations and Applications, 12
Dong Wei (1997)
Uniqueness of solutions for a class of non-linear volterra integral equations without continuityApplied Mathematics and Mechanics, 18
R. Agarwal, D. O’Regan, P. Wong (2004)
Constant-Sign Solutions of a System of Fredholm Integral EquationsActa Applicandae Mathematica, 80
R. Agarwal, D. O’Regan (2000)
Singular Volterra integral equationsAppl. Math. Lett., 13
P. Bushell (1976)
On a class of Volterra and Fredholm non-linear integral equationsMathematical Proceedings of the Cambridge Philosophical Society, 79
D. Reynolds (1984)
On linear singular volterra integral equations of the second kindJournal of Mathematical Analysis and Applications, 103
R.P. Agarwal, D. O’Regan (2002)
Singular integral equations arising in Homann flowDyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 9
Junyu Wang, Wenjie Gao, Zhongxin Zhang (1999)
Singular nonlinear boundary value problems arising in boundary layer theoryJournal of Mathematical Analysis and Applications, 233
P. Nowosad (1966)
On the integral equation κf = 1f arising in a problem in communicationJournal of Mathematical Analysis and Applications, 14
G. Gripenberg, S. Londen, O. Staffans (1990)
Volterra Integral and Functional Equations
M. Meehan, D. O’Regan (2002)
Positive solutions of Volterra integral equations using integral inequalitiesJournal of Inequalities and Applications, 2002
R.P. Agarwal, D. O’Regan, P.J.Y. Wong (2004)
Triple solutions of constant sign for a system of Fredholm integral equationsCubo, 6
Liu Dong, Chen Shanlin (1997)
Snap-buckling of dished shallow shells under uniform loadsApplied Mathematics and Mechanics, 18
C. Corduneanu (1991)
Integral equations and applications
P. Nowosad (1966)
On the integral equation $\kappa f=\frac{1}{f}$ arising in a problem in communicationsJ. Math. Anal. Appl., 14
R. Agarwal (1992)
Opial's and wirtinger's type discrete inequalities in two independent variablesApplicable Analysis, 43
R. Agarwal, D. O’Regan (2003)
Volterra integral equations: the singular caseHokkaido Mathematical Journal, 32
We consider the system of Fredholm integral equations $$\begin{array}{l}\displaystyle u_{i}(t)=\int_{0}^{T}g_{i}(t,s)[h_{i}(s,u_{1}(s),u_{2}(s),\ldots,u_{n}(s))+k_{i}(s,u_{1}(s),u_{2}(s),\ldots,u_{n}(s))]ds,\\[8pt]\quad t\in[0,T],~1\leq i\leq n\end{array}$$ and also the system of Volterra integral equations $$\begin{array}{l}\displaystyle u_{i}(t)=\int_{0}^{t}g_{i}(t,s)[h_{i}(s,u_{1}(s),u_{2}(s),\ldots,u_{n}(s))+k_{i}(s,u_{1}(s),u_{2}(s),\ldots,u_{n}(s))]ds,\\[8pt]\quad t\in[0,T],~1\leq i\leq n\end{array}$$ 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 examples to illustrate the usefulness of the results obtained.
Acta Applicandae Mathematicae – Springer Journals
Published: Apr 15, 2008
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.