E-viri
Recenzirano
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Construction of infinitely many solutions for fractional Schrödinger equation with double potentialsLiu, Ting
Zeitschrift für angewandte Mathematik und Physik, 06/2024, Letnik: 75, Številka: 3Journal Article
We consider the following fractional Schrödinger equation involving critical exponent: ( - Δ ) s u + V ( y ) u = Q ( y ) u 2 s ∗ - 1 , u > 0 , in R N , u ∈ D s ( R N ) , where 2 s ∗ = 2 N N - 2 s , ( y ′ , y ′ ′ ) ∈ R 2 × R N - 2 and V ( y ) = V ( | y ′ | , y ′ ′ ) and Q ( y ) = Q ( | y ′ | , y ′ ′ ) are bounded nonnegative functions in R + × R N - 2 . By using finite-dimensional reduction method and local Pohozaev-type identities, we show that if 2 + N - N 2 + 4 4 < s < min { N 4 , 1 } and Q ( r , y ′ ′ ) has a stable critical point ( r 0 , y 0 ′ ′ ) with r 0 > 0 , Q ( r 0 , y 0 ′ ′ ) > 0 and V ( r 0 , y 0 ′ ′ ) > 0 , then the above problem has infinitely many solutions, whose energy can be arbitrarily large.
