Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero
We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x, a.e. t∈0,1x0cos α−P0x′0sin α=0x1cos β−P1x′1sin β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4221459 |
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| _version_ | 1832546049556742144 |
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| author | Dan Liu Xuejun Zhang Mingliang Song |
| author_facet | Dan Liu Xuejun Zhang Mingliang Song |
| author_sort | Dan Liu |
| collection | DOAJ |
| description | We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x, a.e. t∈0,1x0cos α−P0x′0sin α=0x1cos β−P1x′1sin β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem of Schechter and the symmetric mountain pass theorem of Kajikiya. Applying the results to Sturm–Liouville equations satisfying the mixed boundary value conditions or the Neumann boundary value conditions, we obtain some new theorems and give some examples to illustrate the validity of our results. |
| format | Article |
| id | doaj-art-360072731d414bbeb825a3c272031e27 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-360072731d414bbeb825a3c272031e272025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/42214594221459Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at ZeroDan Liu0Xuejun Zhang1Mingliang Song2Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013, ChinaMathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013, ChinaMathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013, ChinaWe deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x, a.e. t∈0,1x0cos α−P0x′0sin α=0x1cos β−P1x′1sin β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely many solutions by means of the linking theorem of Schechter and the symmetric mountain pass theorem of Kajikiya. Applying the results to Sturm–Liouville equations satisfying the mixed boundary value conditions or the Neumann boundary value conditions, we obtain some new theorems and give some examples to illustrate the validity of our results.http://dx.doi.org/10.1155/2021/4221459 |
| spellingShingle | Dan Liu Xuejun Zhang Mingliang Song Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero Journal of Mathematics |
| title | Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero |
| title_full | Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero |
| title_fullStr | Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero |
| title_full_unstemmed | Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero |
| title_short | Multiple Solutions for Second-Order Sturm–Liouville Boundary Value Problems with Subquadratic Potentials at Zero |
| title_sort | multiple solutions for second order sturm liouville boundary value problems with subquadratic potentials at zero |
| url | http://dx.doi.org/10.1155/2021/4221459 |
| work_keys_str_mv | AT danliu multiplesolutionsforsecondordersturmliouvilleboundaryvalueproblemswithsubquadraticpotentialsatzero AT xuejunzhang multiplesolutionsforsecondordersturmliouvilleboundaryvalueproblemswithsubquadraticpotentialsatzero AT mingliangsong multiplesolutionsforsecondordersturmliouvilleboundaryvalueproblemswithsubquadraticpotentialsatzero |