Finite dimensionality of the kernel and cokernel of quasilinear elliptic mappings

In this work we investigate a certain class of nonlinear mappings of Banach spaces, namely, quasilinear elliptic mappings (q.e.m.'s). Examples of q.e.m.'s are given by mappings which correspond to nonlinear elliptic partial differential equations. For q.e.m.'s of a general form we obtain a theorem which is analogous to a known result on finite dimensionality of the kernel and cokernel of an elliptic linear operator. The results which we obtain are applied to elliptic nonlinear boundary value problems of a general form.
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