Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem
We consider a nonlinear Neumann elliptic equation driven by a \(p\)-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontri...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2015-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol35/6/art/opuscula_math_3545.pdf |
| _version_ | 1811343311904964608 |
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| author | Liliana Klimczak |
| author_facet | Liliana Klimczak |
| author_sort | Liliana Klimczak |
| collection | DOAJ |
| description | We consider a nonlinear Neumann elliptic equation driven by a \(p\)-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations. |
| first_indexed | 2024-04-13T19:27:03Z |
| format | Article |
| id | doaj.art-a889dc571d484218b808ce6b9b47987b |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-04-13T19:27:03Z |
| publishDate | 2015-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-a889dc571d484218b808ce6b9b47987b2022-12-22T02:33:20ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742015-01-01356889905http://dx.doi.org/10.7494/OpMath.2015.35.6.8893545Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problemLiliana Klimczak0Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Krakow, PolandWe consider a nonlinear Neumann elliptic equation driven by a \(p\)-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that the problem has at least two distinct, nontrivial smooth solutions. Our formulation incorporates strongly resonant equations.http://www.opuscula.agh.edu.pl/vol35/6/art/opuscula_math_3545.pdfPalais-Smale conditionnoncoercive functionalsecond deformation theorem |
| spellingShingle | Liliana Klimczak Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem Opuscula Mathematica Palais-Smale condition noncoercive functional second deformation theorem |
| title | Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem |
| title_full | Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem |
| title_fullStr | Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem |
| title_full_unstemmed | Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem |
| title_short | Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem |
| title_sort | existence and multiplicity of solutions for a nonhomogeneous neumann boundary problem |
| topic | Palais-Smale condition noncoercive functional second deformation theorem |
| url | http://www.opuscula.agh.edu.pl/vol35/6/art/opuscula_math_3545.pdf |
| work_keys_str_mv | AT lilianaklimczak existenceandmultiplicityofsolutionsforanonhomogeneousneumannboundaryproblem |