GROUND AND BOUND STATES FOR A STATIC SCHRÖDINGER–POISSON–SLATER PROBLEM

In this paper the following version of the Schrodinger–Poisson–Slater problem is studied: $$-\Delta u + \left ( u^2 \star \frac{1}{|4\pi x|}\right) u=\mu |u|^{p-1}u,$$ where u : ℝ3 → ℝ and μ > 0. The case p 2 we study both the existence of ground and bound states. It turns out that p = 2 is critical in a certain sense, and will be studied separately. Finally, we prove that radial solutions satisfy a point-wise exponential decay at infinity for p > 2.

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