Generalized Choquard Schrodinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces

Abstract: In this work, we discuss the existence of a weak solution for the generalized Choquard Schrodinger equation with vanishing potential. First, we introduce the homogeneous fractional Musielak-Sobolev space and investigate their properties. After that, we discuss the problem in homogeneous fractional Musielak-Sobolev space. To establish our existence results, we prove and use the suitable version of Hardy-Littlewood-Sobolev inequality for Lebesque Musielak spaces together with variational technique based on the mountain pass theorem. We also prove the existence of a ground state solution by the method of Nehari manifold.

 

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Meeting ID: 956 4651 9108
Passcode: 919335