Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN
Abstract
:1. Introduction
2. Preliminaries
- (K1)
- , where ;
- (K2)
- there exist such that for all ;
- (K3)
- for all .
- (V)
- , , for all .
- (F1)
- satisfies the Carathéodory condition.
- (F2)
- There exist non-negative functions and such that
3. Main Result
- (F3)
- For any , there exists constant , such that for , where .
- (F4)
- uniformly for all .
- (D1)
- .
- (D2)
- (D3)
- as .
- (D4)
- I satisfies the -condition for every ,
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Lee, J.I.; Kim, Y.-H.; Lee, J. Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN. Symmetry 2020, 12, 5. https://doi.org/10.3390/sym12010005
Lee JI, Kim Y-H, Lee J. Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN. Symmetry. 2020; 12(1):5. https://doi.org/10.3390/sym12010005
Chicago/Turabian StyleLee, Jun Ik, Yun-Ho Kim, and Jongrak Lee. 2020. "Existence of Small-Energy Solutions to Nonlocal Schrödinger-Type Equations for Integrodifferential Operators in ℝN" Symmetry 12, no. 1: 5. https://doi.org/10.3390/sym12010005