A nonlinear system of volterra integral equations with convolution kernels

Dynamic Systems and Applications

Volumn 14, Issue 1, 2005, Pages 111-120

  Mydlarczyk, Wojciech ^a   Okrasiński, Wojciech ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

A system of nonlinear Volterra integral equations; The blow up solution; The existence of nontrivial solutions

Indexed keywords

CONVOLUTION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

AUXILIARY FUNCTIONS; BLOW-UP SOLUTIONS; EXISTENCE OF NONTRIVIAL SOLUTIONS; SYSTEM OF NONLINEAR VOLTERRA INTEGRAL EQUATIONS;

INTEGRAL EQUATIONS;

EID: 18344374206     PISSN: 10562176     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. P. J. Bushell and W. Okrasiński, Nonlinear Volterra equations and the Apéry identities, Bull. London Math. Soc., 24 (1992), 478-484.
2. F. P. J. Bushell and W. Okrasiński, On the maximal interval of existence for solutions to some nonlinear Volterra integral equations with convolution kernel, Bull. London Math. Soc., 28 (1996), 59-65.
3. G. Gripenberg, Unique solutions of some Volterra integral equations, Math. Scand., 48 (1981), 59-67.
4. G. Gripenberg, S.O. Londen and O. Staffans, Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications 34, Camb. Univ. Press, New York, 1990.
5. D. G. Lesseigne, W.E Olmstead, Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math., 49 (1991), 303-312.
6. W. Mydlarczyk, Remark on nonlinear Volterra equations, Annal. Polon. Math., 53 (1991), 227-232.
7. W. Mydlarczyk, The exitsence of nontrivial solutions of Volterra equations, Math. Scand., 68 (1991), 83-88.
8. W. Mydlarczyk, A condition for finite blow-up time for a Volterra equations, J. Math. Anal. Appl., 181 (1994), 248-253.
9. W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal., 11 (1991), 1007-1015.
10. W. E. Olmstead, C. A. Roberts and K. Deng, Coupled Volterra equations with blow-up solutions, J. Integral Eqns Appl., 7 (1995), 499-516.
11. C. A. Roberts, Analysis of explosion for nonlinear Volterra equations with blow-up solutions, J. Comp. Appl. Math., 97 (1998), 153-166.
12. C. A. Roberts, D. G. Lessigne and W. E. Olmstead Volterra equations which models explosion in a diffusive medium J. Intgeral Equations Apll., 5 (1993), 531-546.