Numerical Computation And Convergence Analysis Of Multi - Solution Problems For Semilinear Elliptic Partial Differential Equations With Inclastic Nonlinear Term

In this thesis, computation on finding multiple solutions of semilinear elliptic equations with concave and convex nonlinearities is discussed. The finite element method is employed to dis-cretize variational problem to get approximation problem. Approximation problem is calculated by the minimax algorithm to capture its multiple solutions. On convergence analysis, global se-quence convergence of computation on approximation problem is established and as diameter of element domain goes to zero, convergence of solutions of the approximation problems to solutions of semilinear elliptic equation is verified.