Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula>
In this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Furthermore, we prove the exis...
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MDPI AG
2022-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/2/38 |
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| author | Kisoeb Park |
| author_facet | Kisoeb Park |
| author_sort | Kisoeb Park |
| collection | DOAJ |
| description | In this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Furthermore, we prove the existence of infinitely many large- or small-energy solutions to this problem with Ambrosetti and Rabinowitz condition. The strategy of the proof for these results is to approach the problem by applying the variational methods, that is, the fountain and the dual fountain theorem with Cerami condition. |
| first_indexed | 2024-03-09T22:37:12Z |
| format | Article |
| id | doaj.art-ea6b5b40cc6b479b904500eba7b253e4 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T22:37:12Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ea6b5b40cc6b479b904500eba7b253e42023-11-23T18:46:40ZengMDPI AGAxioms2075-16802022-01-011123810.3390/axioms11020038Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula>Kisoeb Park0Department of IT Convergence Software, Seoul Theological University, Bucheon 14754, KoreaIn this paper, we establish the existence of a nontrivial weak solution to Schrödinger-kirchhoff type equations with the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Furthermore, we prove the existence of infinitely many large- or small-energy solutions to this problem with Ambrosetti and Rabinowitz condition. The strategy of the proof for these results is to approach the problem by applying the variational methods, that is, the fountain and the dual fountain theorem with Cerami condition.https://www.mdpi.com/2075-1680/11/2/38Schrödinger-kirchhoff equationfractional magnetic operatorsvariational methods |
| spellingShingle | Kisoeb Park Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> Axioms Schrödinger-kirchhoff equation fractional magnetic operators variational methods |
| title | Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> |
| title_full | Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> |
| title_fullStr | Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> |
| title_full_unstemmed | Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> |
| title_short | Multiplicity Results of Solutions to Non-Local Magnetic Schrödinger–Kirchhoff Type Equations in <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow></semantics></math></inline-formula> |
| title_sort | multiplicity results of solutions to non local magnetic schrodinger kirchhoff type equations in inline formula math display inline semantics mrow msup mi mathvariant double struck r mi mi n mi msup mrow semantics math inline formula |
| topic | Schrödinger-kirchhoff equation fractional magnetic operators variational methods |
| url | https://www.mdpi.com/2075-1680/11/2/38 |
| work_keys_str_mv | AT kisoebpark multiplicityresultsofsolutionstononlocalmagneticschrodingerkirchhofftypeequationsininlineformulamathdisplayinlinesemanticsmrowmsupmimathvariantdoublestruckrmiminmimsupmrowsemanticsmathinlineformula |