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Let $f: \mathbb R \rightarrow (-\infty,+\infty]$ be a lower-semicontinuous convex function. Question Under what futher conditions does there exists a convex decreasing function $\phi: \mathbb R \...

I am looking for some maximum principles and comparison results for parabolic equations. The most complete book I've found on this subject is: Murray Protter, Hans Weinberger - Maximum Principles in ...

Basically, I am trying to determine how exactly and in which ways everywhere discontinuous bijections $f: \mathbb R \to \mathbb R$ "behave when they are unusual". More precisely, I am trying to ...

I have an Integro-Differential Equation (IDE) of the following form: $$ x'(t) = f(t,x(t)) + \int_0^t K(t-s, x(s), x(t)) ds, $$ I have found this classical reference, but the IDEs considered therein ...

Let $A,B\subset\mathbb{R}^n, n\geq 2,$ are two different shaped spindles. One is thick and one is thin. (Sorry for my unprofessional statements. Unsure about how to say it rigorously.) So there are ...