A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems
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In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem -u″(x) + m(x)u(x) = λƒ(x, u(x)), x ∈ (α, b), u(α) = u(b) = 0, where λ > 0, ƒ : [α, b] x ℝ → ℝ is a continuous function which changes sign on [α, b] x ℝ and m(x) ∈ C ([α, b]) is a positive function.
CitationAfrouzi, G. A., & Heidarkhani, S. (2006). A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems. Electronic Journal of Differential Equations, 2006(121), pp. 1-10.
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