We study a static version of the Schroedinger–Poisson–Slater equation, with a power nonlinear term. The case when the power p < 2 being already studied, we consider here p ≥ 2. For 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.
Ground and bound states for a static Schrödinger-Poisson-Slater problem / Ianni, I; Ruiz, David. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 14:(2012). [10.1142/S0219199712500034]
Ground and bound states for a static Schrödinger-Poisson-Slater problem
IANNI I;
2012
Abstract
We study a static version of the Schroedinger–Poisson–Slater equation, with a power nonlinear term. The case when the power p < 2 being already studied, we consider here p ≥ 2. For 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.| File | Dimensione | Formato | |
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