A minimax inequality for a class of functionals and applications to the existence of solutions for two-point boundary-value problems
Date
2006-10-02
Authors
Afrouzi, Ghasem Alizadeh
Heidarkhani, Shapour
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Minimax inequality, Critical point, Three solutions, Multiplicity results, Dirichlet problem
Citation
Afrouzi, 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. <i>Electronic Journal of Differential Equations, 2006</i>(121), pp. 1-10.
Rights
Attribution 4.0 International