The three-solutions theorem for -Laplacian boundary value problems

2012 ◽  
Vol 75 (2) ◽  
pp. 924-931 ◽  
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Solutions ◽  
Three Solutions Theorem

Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems

1999 ◽  
Vol 6 (5) ◽  
pp. 415-420
Author(s):  
John M. Davis ◽  
Paul W. Eloe ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Three Solutions ◽  
Continuous Growth ◽  
Order Nonlinear Differential Equation ◽  
Triple Positive Solutions

Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.

Variational approaches to systems of Sturm–Liouville boundary value problems

2020 ◽  
pp. 2150032
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Shahin Moradi
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Technical Approach ◽  
Three Solutions ◽  
Value System ◽  
Sturm Liouville ◽  
Variational Approaches

In this paper, we consider the existence of one solution and three solutions for the boundary value system with Sturm–Liouville boundary conditions [Formula: see text] for [Formula: see text]. Our technical approach is based on variational methods. In addition, examples are provided to illustrate our results.

scholarly journals Existence of three solutions for impulsive nonlinear fractional boundary value problems

2017 ◽  
Vol 37 (2) ◽  
pp. 281 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Massimiliano Ferrara ◽  
Giuseppe Caristi ◽  
Amjad Salari
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Three Solutions ◽  
Fractional Boundary Value Problems

scholarly journals Existence of three solutions to the discrete fourth-order boundary value problem with four parameters

2018 ◽  
Vol 38 (2) ◽  
pp. 173-185 ◽  
Author(s):  
Mohamed Ousbika ◽  
Zakaria El Allali
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Three Solutions

In this work, we willproving the existence of three solutionsf or the discrete nonlinear fourth order boundary value problems with four parameters. The methods used here are based on the critical point theory.

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