On the existence of stationary solutions for some non-Fredholm integro-differential equations

By V. Vougalter, Vitaly Volpert. Documenta Mathematica, 2011

70 citations recorded by the source corpus.

We show the existence of stationary solutions for some reaction-diffusion type equations in the appropriate H2 spaces using the fixed point technique when the elliptic problem contains second order differential operators with and without Fredholm property.

Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/15b0fd2b188b0152a47080d0b2508659767e03bc

Citations in the corpus

• Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems (2012, unknown): “We will be using the closed unit ball centered at the origin in the Sobolev space with the norm defined in (4.8): B(H 2 (R d )) = {u(x) ∈ H 2 (R d ) | u H 2 (R d ) ≤ 1}, (1.21) as distinct from the results obtained in the whole space in [18].”