Abstract
Let E be a real separable Banach space, E ∗ the dual space of E, and Ω ⊂ E an open bounded subset, and let T : D ( T ) ⊆ E → 2 E ∗ be a finite dimensional upper hemi-continuous mapping with D ( T ) ∩ Ω ≠ ∅ . A generalized degree theory is constructed for such a mapping. This degree is then applied to study the existence of approximate weak solutions to the equation 0 ∈ Tx .
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