On ground state for a class of nonlinear Schrödinger equation
I study the existence of ground state for the following periodic Schrödinger equation under the circumstance that the nonlinear term satisfies odd conditions by using the Mountain Pass Lemma and variational method. $$-\Delta u+V(x)u-\Delta(1+u^2)^{{1}/{2}}{u\over 2(1+u^2)^{{1}/{2}}}=f\,(x, u).$$
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-03-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | http://dx.doi.org/10.1080/16583655.2018.1451058 |