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Multiplicity of radial and nonradial solutions to equations with fractional operators

The author is supported by JSPS KAKENHI Grant Number JP16K17623 and JP17H02851
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  • In this paper, we study the existence of radial and nonradial solutions to the scalar field equations with fractional operators. For radial solutions, we prove the existence of infinitely many solutions under $ N \geq 2 $. We also show the existence of least energy solution (with the Pohozaev identity) and its mountain pass characterization. For nonradial solutions, we prove the existence of at least one nonradial solution under $ N \geq 4 $ and infinitely many nonradial solutions under either $ N = 4 $ or $ N \geq 6 $. We treat both of the zero mass and the positive mass cases.

    Mathematics Subject Classification: Primary: 35J20, 35J60.

    Citation:

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