Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential
In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrödinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with <inline-formula><math xmlns="http://www.w3.org/1998/Math/Mat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-08-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/15/2736 |
| Summary: | In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrödinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>. By considering a constrained variational problem, we first establish the existence of ground state solutions. Then, we prove the asymptotic behaviors of the solutions as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>→</mo><msup><mn>0</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>. The main ingredients of the proofs are some energy estimate arguments. Our results improve somewhat the ones in the existing reference. |
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| ISSN: | 2227-7390 |