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Instability of solutions to nonlinear systems
In this post, we propose two results in the instability of solutions to nonlinear systems. Here, we study ordinary differential equations. Well-know stability theorems...
Direct sum of subspaces examples
The philosophy behind the direct sum of subspaces is the decomposition of vector spaces as a sum of disjoint spaces. In fact, this is...
Open mapping theorem in functional analysis
In this article, we give an application of the open mapping theorem in functional analysis. This fundamental theorem in functional analysis plays a key...
Differential calculus in Banach spaces
Differential calculus in Banach spaces is a very important part of mathematics. In fact, the treatment of partial differential equations strongly depends on this...
Heat equation using the Fourier series
In this article, we learn how to solve the heat equation using the Fourier series. The heat equation belongs to the class of partial...
Gronwall lemma
In this article, we state and prove Gronwall lemma and give some of its applications. In fact, we will use this lemma for the...