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Generalizations of the Lax-Milgram theorem. (English) Zbl 1140.47303

Summary: We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.

MSC:

47A07 Forms (bilinear, sesquilinear, multilinear)
47H60 Multilinear and polynomial operators
35J60 Nonlinear elliptic equations
46B99 Normed linear spaces and Banach spaces; Banach lattices
47N20 Applications of operator theory to differential and integral equations
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References:

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