Abstract
In the present paper, numerical solving of the double-periodic elliptic eigenvalue problems Mu,l:=Du +lu+fu =0 0≤x<2p,0≤ y<2p3 is considered regarding special symmetry properties. At first, subspaces V with the desired symmetry are constructed then a classical Ritz method is applied for the discretization in V and the resulting finite-dimensional bifurcation problem is solved by an algorithm proposed by Keller and Langford representing a numerical implementation of the Ljapunov-Schmidt procedure. If f(u) is an entire function or a polynomial and V is an algebra then the computed solutions reveal to be stable with respect to perturbations of less symmetry. Some examples demonstrate the efficiency of the procedure. —Author's Abstract
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