Fixed Point Theorems and Applications in PDEs

Fixed Point Theorems and Applications in PDEs

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Shiwu Yang
Fine Hall 314

I'll begin with Banach's fixed point theorem in which strict contraction is required and then give examples to show how this simple theorem implies the local and global existence to vary kinds of evolution equations. I'll also introduce Schauder and Schaefer's fixed point theorem which would be of importance in elliptic theory and verify this by several examples if time permitted.