Convex sets and second order systems with nonlocal boundary conditions at resonance
(2017) Proceedings of the American Mathematical Society — Vol. 145, n° 5, p. 2023-2032 (2017)
Files
No attached file found for this publication.
Details
- Authors
- Abstract
- The solvability of the resonant nonlocal boundary value problem (Formula presented.) with f: [0, 1] × Rn × Rn → Rn continuous, g = diag(g1,…, gn), gi: [0, 1] → R of bounded variation, (Formula presented.), is studied using the Leray-Schauder continuation theorem. The a priori estimates follow from the existence of an open bounded convex subset C ⊂ Rn, such that, for each t ∈ [0, 1] and x ∈ C, the vector fields f(t, x, ·) satisfy suitable geometrical conditions on ∂C. The special cases where C is a ball or a parallelotope are considered.
- Affiliations
Citations
Mawhin, J., & Szymańska-Dȩbowska, K. (2017). Convex sets and second order systems with nonlocal boundary conditions at resonance. Proceedings of the American Mathematical Society, 145(5), 2023-2032. https://doi.org/10.1090/proc/13569 (Original work published 2017)