Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations
In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...
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2024-11-01
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| author | Ruoyi Liu Zhan Zhou |
| author_facet | Ruoyi Liu Zhan Zhou |
| author_sort | Ruoyi Liu |
| collection | DOAJ |
| description | In this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>. Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for this problem and obtain some determined open intervals of the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> for the existence of at least two positive solutions. In the end, we give two examples to illustrate our main results. |
| format | Article |
| id | doaj-art-40d4cf582b534eceaf3074fbafa2d0c4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-40d4cf582b534eceaf3074fbafa2d0c42024-12-13T16:27:41ZengMDPI AGMathematics2227-73902024-11-011223377010.3390/math12233770Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference EquationsRuoyi Liu0Zhan Zhou1School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaIn this paper, we investigate positive solutions of boundary value problems for a general second-order nonlinear difference equation, which includes a Jacobi operator and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>. Based on the critical point theory, we obtain the existence of three solutions for the boundary value problem. Then, we establish a strong maximum principle for this problem and obtain some determined open intervals of the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> for the existence of at least two positive solutions. In the end, we give two examples to illustrate our main results.https://www.mdpi.com/2227-7390/12/23/3770boundary value problemtwo positive solutionscritical point theorynonlinear difference equations |
| spellingShingle | Ruoyi Liu Zhan Zhou Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations Mathematics boundary value problem two positive solutions critical point theory nonlinear difference equations |
| title | Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations |
| title_full | Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations |
| title_fullStr | Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations |
| title_full_unstemmed | Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations |
| title_short | Positive Solutions of Boundary Value Problems for General Second-Order Nonlinear Difference Equations |
| title_sort | positive solutions of boundary value problems for general second order nonlinear difference equations |
| topic | boundary value problem two positive solutions critical point theory nonlinear difference equations |
| url | https://www.mdpi.com/2227-7390/12/23/3770 |
| work_keys_str_mv | AT ruoyiliu positivesolutionsofboundaryvalueproblemsforgeneralsecondordernonlineardifferenceequations AT zhanzhou positivesolutionsofboundaryvalueproblemsforgeneralsecondordernonlineardifferenceequations |