(p,2)-equations asymmetric at both zero and infinity
We consider a (p,2){(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with p>2{p>2}. The reaction term is (p-1){(p-1)}-linear, but exhibits asymmetric behavior at ±∞{\pm\infty} and at 0±{0^{\pm}}. Using variational tools,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-08-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2017-0195 |
| _version_ | 1819293396839170048 |
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| author | Papageorgiou Nikolaos S. Rădulescu Vicenţiu D. Repovš Dušan D. |
| author_facet | Papageorgiou Nikolaos S. Rădulescu Vicenţiu D. Repovš Dušan D. |
| author_sort | Papageorgiou Nikolaos S. |
| collection | DOAJ |
| description | We consider a (p,2){(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with p>2{p>2}. The reaction term is (p-1){(p-1)}-linear, but exhibits asymmetric behavior at ±∞{\pm\infty} and at 0±{0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal). |
| first_indexed | 2024-12-24T04:09:46Z |
| format | Article |
| id | doaj.art-46d5c1c96411460e922a5273fcffee69 |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-24T04:09:46Z |
| publishDate | 2018-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-46d5c1c96411460e922a5273fcffee692022-12-21T17:16:05ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2018-08-017332735110.1515/anona-2017-0195(p,2)-equations asymmetric at both zero and infinityPapageorgiou Nikolaos S.0Rădulescu Vicenţiu D.1Repovš Dušan D.2Department of Mathematics, National Technical University, Zografou Campus, Athens15780, GreeceInstitute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700Bucharest; and Department of Mathematics, University of Craiova, 200585 Craiova, RomaniaFaculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, SI-1000Ljubljana, SloveniaWe consider a (p,2){(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with p>2{p>2}. The reaction term is (p-1){(p-1)}-linear, but exhibits asymmetric behavior at ±∞{\pm\infty} and at 0±{0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).https://doi.org/10.1515/anona-2017-0195asymmetric reactionresonancefučik spectrumconstant sign solutionsnodal solutioncritical groupsmorse relation35j20 35j60 58e05 |
| spellingShingle | Papageorgiou Nikolaos S. Rădulescu Vicenţiu D. Repovš Dušan D. (p,2)-equations asymmetric at both zero and infinity Advances in Nonlinear Analysis asymmetric reaction resonance fučik spectrum constant sign solutions nodal solution critical groups morse relation 35j20 35j60 58e05 |
| title | (p,2)-equations asymmetric at both zero and infinity |
| title_full | (p,2)-equations asymmetric at both zero and infinity |
| title_fullStr | (p,2)-equations asymmetric at both zero and infinity |
| title_full_unstemmed | (p,2)-equations asymmetric at both zero and infinity |
| title_short | (p,2)-equations asymmetric at both zero and infinity |
| title_sort | p 2 equations asymmetric at both zero and infinity |
| topic | asymmetric reaction resonance fučik spectrum constant sign solutions nodal solution critical groups morse relation 35j20 35j60 58e05 |
| url | https://doi.org/10.1515/anona-2017-0195 |
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