Variational Methods and Monotonicity.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Nonlinear equations and variational inequalities in reflexive Banach spaces are considered using the concept of pseudomonotone operators of H. Brezis. The existence theory is based on finite dimensional approximations solved by using Brouwer fixed point theorem and a limiting procedure requiring weak continuity properties. Some continuous dependence properties are given and applied to the penalization method. Then some examples are studied corresponding to heat diffusion. Finally some results on Hammerstein equations are derived.
- Theoretical Mathematics