The Existence and Local Uniqueness of Multi-Peak Solutions to a Class of Kirchhoff Type Equations

摘要

In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations @@@ [GRAPHICS] @@@ . @@@ which concentrate at non-degenerate critical points of the potential function V (x), where a, b > 0, 1 < p < 5 are constants, and epsilon > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existence and local uniqueness results of multi-peak solutions, which concentrate at {ai}(1 <= i <= k), where {ai}(1 <= i <= k) are non-degenerate critical points of V (x) as is an element of -> 0.

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