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monotone operators; weakly continuous operators; existence theorems; boundary value problems for differential equations; heat conduction equation; Navier-Stokes equations
The paper is a supplement to a survey by J. Franců: Monotone operators, A survey directed to differential equations, Aplikace Matematiky, 35(1990), 257–301. An abstract existence theorem for the equation $Au = b$ with a coercive weakly continuous operator is proved. The application to boundary value problems for differential equations is illustrated on two examples. Although this generalization of monotone operator theory is not as general as the M-condition, it is sufficient for many technical applications.
[1] J. Franců: Monotone operators, Survey directed to differential equations. Aplikace matematiky 35 (1990), 257–301. MR 1065003
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