EXISTENCE AND CONCENTRATION OF GROUND STATE SOLUTION TO A CRITICAL p–LAPLACIAN EQUATION
نویسندگان
چکیده
In this paper, we consider the existence and concentration behavior of positive ground state solution to the following problem { −hΔpu+V (x)|u|p−2u = K(x)|u|q−2u+ |u|p−2u, x ∈ RN , u ∈W 1,p(RN ), u > 0, x ∈ RN , where h is a small positive parameter, 1 < p < N , max{p, p∗ − p p−1} < q < p∗ , p∗ = Np N−p is the critical Sobolev exponent, V (x) and K(x) are positive smooth functions. Under some necessary restrictions, we show that for small h > 0 , the equation has a positive ground state solution. Furthermore, we establish the concentration property of such solutions when h tends to zero. Mathematics subject classification (2010): 35J92, 35J35.
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