Vol. 60, No. 1, 1975

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Monotone operators and nonlinear biharmonic boundary value problems

Dennis Robert Dunninger and John Stewart Locker

Vol. 60 (1975), No. 1, 39–48
Abstract

The nonlinear boundary value problem Lu + Nu = 0 is considered, where L is the biharmonic operator and N is a nonlinear monotone operator. By factoring the operator L as TT, where T is the maximal operator associated with the Laplacian, the theory of monotone operators is utilized to obtain an existence and uniqueness theorem for the operator equation. SeveraI examples are given to illustrate the applicability of the resu1t.

Mathematical Subject Classification 2000
Primary: 47H15
Secondary: 35G30
Milestones
Received: 10 June 1974
Published: 1 September 1975
Authors
Dennis Robert Dunninger
John Stewart Locker