Multiple solutions to the double phase problems involving concave-convex nonlinearities
This paper is concerned with several existence results of multiple solutions for Schrödinger-type problems involving the double phase operator for the case of a combined effect of concave-convex nonlinearities. The first one is to discuss that our problem has infinitely many large energy solutions....
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023254?viewType=HTML |
| _version_ | 1811176578781020160 |
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| author | Jae-Myoung Kim Yun-Ho Kim |
| author_facet | Jae-Myoung Kim Yun-Ho Kim |
| author_sort | Jae-Myoung Kim |
| collection | DOAJ |
| description | This paper is concerned with several existence results of multiple solutions for Schrödinger-type problems involving the double phase operator for the case of a combined effect of concave-convex nonlinearities. The first one is to discuss that our problem has infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the given problem. To establish such multiplicity results, we employ the fountain theorem and the dual fountain theorem as the primary tools, respectively. In particular we give the existence result of small energy solutions on a new class of nonlinear term. |
| first_indexed | 2024-04-10T19:53:51Z |
| format | Article |
| id | doaj.art-5ab7aff8647443ddb04c2360e80a827f |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T19:53:51Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5ab7aff8647443ddb04c2360e80a827f2023-01-28T01:07:45ZengAIMS PressAIMS Mathematics2473-69882023-01-01835060507910.3934/math.2023254Multiple solutions to the double phase problems involving concave-convex nonlinearitiesJae-Myoung Kim0Yun-Ho Kim11. Department of Mathematics Education, Andong National University, Andong 36729, Korea2. Department of Mathematics Education, Sangmyung University, Seoul 03016, KoreaThis paper is concerned with several existence results of multiple solutions for Schrödinger-type problems involving the double phase operator for the case of a combined effect of concave-convex nonlinearities. The first one is to discuss that our problem has infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the given problem. To establish such multiplicity results, we employ the fountain theorem and the dual fountain theorem as the primary tools, respectively. In particular we give the existence result of small energy solutions on a new class of nonlinear term.https://www.aimspress.com/article/doi/10.3934/math.2023254?viewType=HTMLdouble phase problemsmusielak-orlicz-sobolev spacesvariational methodsmultiple solutions |
| spellingShingle | Jae-Myoung Kim Yun-Ho Kim Multiple solutions to the double phase problems involving concave-convex nonlinearities AIMS Mathematics double phase problems musielak-orlicz-sobolev spaces variational methods multiple solutions |
| title | Multiple solutions to the double phase problems involving concave-convex nonlinearities |
| title_full | Multiple solutions to the double phase problems involving concave-convex nonlinearities |
| title_fullStr | Multiple solutions to the double phase problems involving concave-convex nonlinearities |
| title_full_unstemmed | Multiple solutions to the double phase problems involving concave-convex nonlinearities |
| title_short | Multiple solutions to the double phase problems involving concave-convex nonlinearities |
| title_sort | multiple solutions to the double phase problems involving concave convex nonlinearities |
| topic | double phase problems musielak-orlicz-sobolev spaces variational methods multiple solutions |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023254?viewType=HTML |
| work_keys_str_mv | AT jaemyoungkim multiplesolutionstothedoublephaseproblemsinvolvingconcaveconvexnonlinearities AT yunhokim multiplesolutionstothedoublephaseproblemsinvolvingconcaveconvexnonlinearities |