What do we call the PDE problems in the form of $\Delta u + \epsilon u = f$ on Sobolev spaces

49 Views Asked by At

I'm studying the existence and uniqueness of a solution and its asymptotic behaviour to the following problem

\begin{align} & -\Delta u +\epsilon u = f \text{ on } \Omega \\ & \dfrac{\partial u}{\partial \nu}= g \text{ on } \Gamma \end{align}

through variational formulations and Sobolev spaces.

Where $\Omega$ is the domain, $\Gamma$ its border and $\epsilon > 0$.

Does anyone know where I can find resources for this type of problem ? Thanks.