Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth
In this paper, we investigate a perturbed elliptic boundary value problem that exhibits critical growth characterized by a Trudinger–Moser-type inequality. Our primary focus is to establish the existence of two nontrivial solutions. This is achieved by employing a combination of the Trudinger–Moser-...
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2024-10-01
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| author | Sheng Shi Yang Yang |
| author_facet | Sheng Shi Yang Yang |
| author_sort | Sheng Shi |
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| description | In this paper, we investigate a perturbed elliptic boundary value problem that exhibits critical growth characterized by a Trudinger–Moser-type inequality. Our primary focus is to establish the existence of two nontrivial solutions. This is achieved by employing a combination of the Trudinger–Moser-type inequality and a linking theorem based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></semantics></math></inline-formula>-cohomological index. The main feature and novelty of this paper lies in extending the equation to <i>N</i>-Laplacian boundary value problems utilizing the aforementioned methods. This extension not only broadens the applicability of these techniques but also enriches the research outcomes in the field of nonlinear analysis. |
| format | Article |
| id | doaj-art-f425da9994f84151a6ff37da457bac74 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-10-01 |
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| series | Axioms |
| spelling | doaj-art-f425da9994f84151a6ff37da457bac742024-11-26T17:50:44ZengMDPI AGAxioms2075-16802024-10-01131173310.3390/axioms13110733Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical GrowthSheng Shi0Yang Yang1School of Science, Jiangnan University, Wuxi 214122, ChinaSchool of Science, Jiangnan University, Wuxi 214122, ChinaIn this paper, we investigate a perturbed elliptic boundary value problem that exhibits critical growth characterized by a Trudinger–Moser-type inequality. Our primary focus is to establish the existence of two nontrivial solutions. This is achieved by employing a combination of the Trudinger–Moser-type inequality and a linking theorem based on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></semantics></math></inline-formula>-cohomological index. The main feature and novelty of this paper lies in extending the equation to <i>N</i>-Laplacian boundary value problems utilizing the aforementioned methods. This extension not only broadens the applicability of these techniques but also enriches the research outcomes in the field of nonlinear analysis.https://www.mdpi.com/2075-1680/13/11/733<i>N</i>-Laplaciancritical growthlinking theoremperturbationℤ<sub>2</sub>-cohomological index |
| spellingShingle | Sheng Shi Yang Yang Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth Axioms <i>N</i>-Laplacian critical growth linking theorem perturbation ℤ<sub>2</sub>-cohomological index |
| title | Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth |
| title_full | Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth |
| title_fullStr | Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth |
| title_full_unstemmed | Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth |
| title_short | Existence of Solutions for a Perturbed <i>N</i>-Laplacian Boundary Value Problem with Critical Growth |
| title_sort | existence of solutions for a perturbed i n i laplacian boundary value problem with critical growth |
| topic | <i>N</i>-Laplacian critical growth linking theorem perturbation ℤ<sub>2</sub>-cohomological index |
| url | https://www.mdpi.com/2075-1680/13/11/733 |
| work_keys_str_mv | AT shengshi existenceofsolutionsforaperturbedinilaplacianboundaryvalueproblemwithcriticalgrowth AT yangyang existenceofsolutionsforaperturbedinilaplacianboundaryvalueproblemwithcriticalgrowth |