Studies On Multiple Solutions Of A Class Of Volterra Integral Equations With Weakly Singular Kernel

Integral equations can be used to model phenomena in many application fields such as physics,mechanics,electricity and microwave technology.The study of such equations,particularly the second-kind VIEs has been gaining much attention from more and more mathematicians.On the basis of Han's study on a special second-kind VIEs,this thesis studies a more common one with weakly singular kernel.The considered second-kind VIEs with weakly singular kernel comes from physical models with memory material and also have applications in some fields such as fluid mechanics and biomedicine.The main content of this paper is: 1.investigate the multiple solutions of the second-kind VIEs with weakly singular kernel;2.numerically solve the equations.This thesis is organized in the following five chapters:In the first chapter,we introduces the research background and current research status of the considered problem and describe the innovation method and preliminary knowledge of this thesis.In the second chapter,we give a unified representation of the solutions to the VIEs with weakly singular kernel.In the third chapter,using Taylor Theory we design a numerical scheme to solve the VIEs with infinite solutions and prove the first order convergence rate.In the fourth chapter,we provide several numerical tests to confirm our theoretical findings;In the final section,we draw conclusion and discuss the future work.