A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum
We consider the nonlinear Schrödinger equation -Δu+f(u)=V(x)u in RN. The potential function V satisfies that the essential spectrum of the Schrödinger operator -Δ-V is [0,+∞) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearity f satisfies t...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/3042493 |
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| _version_ | 1832547284198359040 |
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| author | Shaowei Chen Haijun Zhou |
| author_facet | Shaowei Chen Haijun Zhou |
| author_sort | Shaowei Chen |
| collection | DOAJ |
| description | We consider the nonlinear Schrödinger equation -Δu+f(u)=V(x)u in RN. The potential function V satisfies that the essential spectrum of the Schrödinger operator -Δ-V is [0,+∞) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearity f satisfies the resonance type condition limt→∞f(t)/t=0. Under some additional conditions on V and f, we prove that this equation has infinitely many solutions. |
| format | Article |
| id | doaj-art-54c470c06f484b949517e652939879f8 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-54c470c06f484b949517e652939879f82025-02-03T06:45:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/30424933042493A Nonlinear Schrödinger Equation Resonating at an Essential SpectrumShaowei Chen0Haijun Zhou1School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaSchool of Mathematical Sciences, Huaqiao University, Quanzhou 362021, ChinaWe consider the nonlinear Schrödinger equation -Δu+f(u)=V(x)u in RN. The potential function V satisfies that the essential spectrum of the Schrödinger operator -Δ-V is [0,+∞) and this Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. The nonlinearity f satisfies the resonance type condition limt→∞f(t)/t=0. Under some additional conditions on V and f, we prove that this equation has infinitely many solutions.http://dx.doi.org/10.1155/2016/3042493 |
| spellingShingle | Shaowei Chen Haijun Zhou A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum Advances in Mathematical Physics |
| title | A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum |
| title_full | A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum |
| title_fullStr | A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum |
| title_full_unstemmed | A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum |
| title_short | A Nonlinear Schrödinger Equation Resonating at an Essential Spectrum |
| title_sort | nonlinear schrodinger equation resonating at an essential spectrum |
| url | http://dx.doi.org/10.1155/2016/3042493 |
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