We consider a semilinear elliptic operator P on a manifold B with a conical singular point. We assume P is Fuchs type in the linear part and has a non-linear lower order therms. Using the Schauder fixed point theorem, we prove the local solvability of P near the conical point in the weighted Sobolev spaces.
Local solvability for semilinear Fuchsian equations / F. Messina. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 257(2003), pp. 67-86.
Local solvability for semilinear Fuchsian equations
F. MessinaPrimo
2003
Abstract
We consider a semilinear elliptic operator P on a manifold B with a conical singular point. We assume P is Fuchs type in the linear part and has a non-linear lower order therms. Using the Schauder fixed point theorem, we prove the local solvability of P near the conical point in the weighted Sobolev spaces.
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