Existence of solutions to n-dimensional pendulum-like equations
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We study the elliptic boundary-value problem
∆u + g(x, u) = p(x) in Ω
u|∂Ω = constant, ∫∂Ω ∂u/∂v = 0,
where g is T-periodic in u, and Ω ⊂ ℝn is a bounded domain. We prove the existence of a solution under a condition on the average of the forcing term p. Also, we prove the existence of a compact interval Ip ⊂ ℝ such that the problem is solvable for p̃(x) = p(x) + c if and only if c ∈ Ip.
CitationAmster, P., De Nápoli, P. L., & Mariani, M. C. (2004). Existence of solutions to n-dimensional pendulum-like equations. Electronic Journal of Differential Equations, 2004(125), pp. 1-8.
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