Structure of the set of solutions of an initial-boundary value problem for a parabolic partial differential equation in an unbounded domain

A Wave Equation Associated with Mixed Nonhomogeneous Conditions: The Compactness and Connectivity of Weak Solution Set

“…We show here that the set of solutions of (1.1)-(1.2) is nonempty and satisfies the classical Hukuhara-Kneser property, that is, the set of solutions is a compact connected set in an appropriate function space. Such structure of the solutions set for differential equations was studied in [6][7][8][9][10], we mention here [8][9][10] for Hukuhara-Kneser property and [6,7] for R δ -structure. It is well known that the "R δ " results are really stronger than classical Kneser-type theorems, see [6,7].…”

A continuum of solutions in a Fréchet space of a nonlinear functional integral equation in N variables

“…Such a structure of solutions set for differential equations and integral equations have been studied by many authors, for examples, we refer to , , , , –, and references therein. We mention here , , for Hukuhara–Kneser property and , , , for ‐structure. In , solution sets of abstract, Volterra, functional and functional differential equations in appropriate Fréchet spaces were discussed and applications to integral and integrodifferential equations and initial value problems were examined.…”