Certain nonlocal boundary-value problems for linear differential operators
A theorem of existence and uniqueness is proved for the elliptic equation \(Au=f\) (in \(G\subset {\mathbb{R}}^ n\), \(n>1)\) \(u=\phi\) on \({\bar \Gamma}{}_ 0\), \(bu+Bu=\psi\) on \({\bar \Gamma}\), \(b\in C({\bar \Gamma})\), \(b\neq 0\), \(\Gamma_ 0\cap =\emptyset\), \(\Gamma_ 0\cup \Gamma \cup \gamma =\partial G\), \(\gamma =\partial \Gamma_ 0=\partial \Gamma\), \(\phi,\psi\in C\) and f is Hölderian; \(B: C(\bar G)\to C({\bar \Gamma})\) and is of the form \((Bu)(u)=\sum_{j}\int_{G}u(y)\mu_ j(x,dy)\) where \(\mu_ j: {\bar \Gamma}\to C(\bar G)\), \(j=1,2,..\). are continuous transformations of \({\bar \Gamma}\) in the space of measures on \(\bar G.\)
scientific article; zbMATH DE number 3881128