Abstract
We consider the following singularly perturbed nonlocal elliptic problem
where \(\varepsilon >0\) is a parameter, \(a>0,b\ge 0\) are constants, \(\alpha \in (0,3)\), \(p\in [2, 6-\alpha )\), \(W_{\alpha }(x)\) is a convolution kernel and V(x) is an external potential satisfying some conditions. By using variational methods, we establish the existence and concentration of positive ground state solutions for the above equation.
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The author is grateful to Professor Shuangjie Peng for his helpful suggestions and careful guidance.
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Communicated by A. Jüngel.
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Lü, D. Existence and concentration of ground state solutions for singularly perturbed nonlocal elliptic problems. Monatsh Math 182, 335–358 (2017). https://doi.org/10.1007/s00605-016-0889-x
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DOI: https://doi.org/10.1007/s00605-016-0889-x
Keywords
- Kirchhoff-type equation
- Hartree-type nonlinearity
- Variational method
- Ground state solution
- Concentration phenomena