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On a Nonlocal Boundary Value Problem at Resonance
Let \(E\) be the interval \([0,1]\) of \(\mathbb{R}\) and let \(N:C^1(E,\mathbb{R}) \rightarrow L^1(E,\mathbb{R})\) be a continuous operator. The authors study the existence of solutions to the initial value problem \[ Lx(t)=x''(t)=Nx(t), \text{ a.a.t.
P Ch Tsamatos
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A Nonlocal Vector Calculus With Application to Nonlocal Boundary Value Problems
Multiscale Modeling and Simulation, 2010We develop a calculus for nonlocal operators that mimics Gauss's theorem and Green's identities of the classical vector calculus. The operators we define do not involve derivatives. We then apply the nonlocal calculus to define weak formulations of nonlocal “boundary-value” problems that mimic the Dirichlet and Neumann problems for second-order scalar ...
Max Gunzburger
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