On the existence and multiplicity of solutions for the $ N $-Choquard logarithmic equation with exponential critical growth

Author name not available (Why is that?)

Publication date: 14 March 2021

Abstract: In the present work we briefly explain how to adapt techniques already used in fractional and

p

-fractional Laplacian cases to obtain the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution, for the critical case, and the existence of infinitely many solutions, for the subcritical case, to the Choquard Logarithmic equation,

- D e l t a_{N} u + a (x) | u |^{N - 2} u + l a m b d a (l n | c d o t | a s t | u |^{N}) | u |^{N - 2} u = f (u) e x t r m i n m a t h b b R^{N}

, where

a : m a t h b b R^{N} i g h t a r r o w m a t h b b R

,

l a m b d a > 0

,

N g e q 3

and

f : m a t h b b R i g h t a r r o w [0, i n f t y)

is continuous function that behaves like

e x p (a l p h a | u |^{f r a c N N - 1})

at infinity, for

a l p h a > 0

.

Mathematics Subject Classification ID

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