Vol. 44, No. 2, 1973

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A nonlinear elliptic boundary value problem

Stephen Andrew Williams

Vol. 44 (1973), No. 2, 767–774

This paper proves that there is a (weak) solution u (not necessarily unique) to the generalized Dirichlet problem (with null boundary data) for the equation Au + pu = h. Here A is a strongly and uniformly elliptic operator of order 2m on a bounded open set Ω Rn. Also A is “normal”: roughly, AA = AA. The functions p and h are bounded and continuous, but are allowed to depend on x(x Ω),u, and the generalized derivatives of u up to order m. The values of p are restricted to lie in a closed disk of the complex plane which contains the negative of no weak eigenvalue of A.

Mathematical Subject Classification 2000
Primary: 35J60
Received: 13 September 1971
Published: 1 February 1973
Stephen Andrew Williams