Abstract
We are concerned with the multiplicity of positive and nodal solutions of{−Δu+μu=Q(x)|u|p−2uinℝNu∈H1(ℝN) where 2<p<2NN−2, N ≥ 3, μ > 0, Q ∈ C(ℝN) and Q(x) ≥ 0 for x ∈ ℝN. We show how the “shape” of the graph of Q(x) affects the number of both positive and nodal solutions.
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