Details

Autor(en) / Beteiligte

• Liu, Zhisu
• Rădulescu, Vicenţiu D.
• Yuan, Ziqing

Titel

Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction

Ist Teil von

• Zeitschrift für angewandte Mathematik und Physik, 2022-10, Vol.73 (5), Article 211

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2022

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, we consider the following fractional Kirchhoff equation with discontinuous nonlinearity ε 2 α a + ε 4 α - 3 b ∫ R 3 | ( - Δ ) α 2 u | 2 d x ( - Δ ) α u + V ( x ) u = H ( u - β ) f ( u ) in R 3 , u ∈ H α ( R 3 ) , u > 0 in R 3 , where ε , β > 0 are small parameters, α ∈ ( 3 4 , 1 ) and a ,  b are positive constants, ( - Δ ) α is the fractional Laplacian operator, H is the Heaviside function, V is a positive continuous potential, and f is a superlinear continuous function with subcritical growth. By using minimax theorems together with the non-smooth theory, we obtain existence and concentration properties of positive solutions to this non-local system.