Existence of solutions to N-dimensional pendulum-like equations
We study the elliptic boundary-value problem Δu + g(x, u) = p(x) in Ω u| ∂Ω = constant, ∫ ∂Ω ∂u/∂ν = 0, where g is T-periodic in u, and Ω ⊂ ℝ n 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...
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| Autores principales: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10726691_v2004_n_p1_Amster |
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| Sumario: | We study the elliptic boundary-value problem Δu + g(x, u) = p(x) in Ω u| ∂Ω = constant, ∫ ∂Ω ∂u/∂ν = 0, where g is T-periodic in u, and Ω ⊂ ℝ n 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 I p ⊂ ℝ such that the problem is solvable for p̃(x) = p(x) + c if and only if c ∈ I p. |
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