INTEGRAL EQUATIONS

Author: BENÍTEZ SUÁREZ RAFAEL.
Year: 2003.
University: EXTREMADURA [www.unex.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In this thesis are studied nonlinear equations of Voltera, of the second kind, and with uniform nuclei convolución.Se discusses various characterizations of the existence of solutions bounded near cero.Se results extend known locally bounded uniqueness of solutions to positive solutions in the case where the core of the equation is a function locally bounded. Also discussed in this case the nature of attractor global solutions locally bounded. The equations are then analyzed by Abel nuclei with non - locally bounded by extending the first results on the nature of attractor solutions bounded near zero and enontrando examples of Abel equations with solutions locally bounded (with a asíntota in origin). Based on these equations Abel with two solutions prositivas: a locally bounded and other non - locally acotada.En these cases are discussed also the attractor of these solutions, seeing that, contrary to what happens with the locally bounded solutions, have no a character attractor.

Author: BENÍTEZ SUÁREZ RAFAEL.
Year: 2003.
University: EXTREMADURA [www.unex.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In this thesis are studied nonlinear equations of Volterra, of the second kind, homogeneous and convolution kernels. It discusses various characterizations of the existence of solutions bounded near zero. They straddle results known uniqueness of positive solutions in the event that the core of the equation is a function locally bounded. Also discussed in this case the nature of attractor global solutions locally bounded. The equations are then analyzed by Abel nuclei with non - locally bounded by extending the first results on the nature aractor of solutions bounded near zero and finding examples of Abel equations with solutions locally bounded (with a asíntota in origin). Based on these equations are constructed other examples of equations Abel with two positive solutions: a locally bounded and other non - locally bounded. In these cases also analyzes the attractor of these solutions, seeing that, contrary to what happens with the locally bounded solutions, not on a attractor.