Positive solutions for a quasilinear Schrödinger equation
نویسندگان
چکیده
We consider the quasilinear problem −εpdiv(|∇u|p−2∇u) + V (z)up−1 = f(u) + up−1, u ∈W (R ), where ε > 0 is a small parameter, 1 < p < N , p∗ = Np/(N − p), V is a positive potential and f is a superlinear function. Under a local condition for V we relate the number of positive solutions with the topology of the set where V attains its minimum. In the proof we apply Ljusternik-Schnirelmann theory. 2000 Mathematics Subject Classification : 35J50, 35B33, 58E05.
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