On a periodic Schrödinger equation with nonlocal superlinear part

By Nils Ackermann. 2004

268 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cce4d297912be2d0cb582aab0094a908146181de

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations (2006, methodology): “2 for Φ, which can be proved under our present conditions on Φ (see [1]).”
Positive and sign changing solutions to a nonlinear Choquard equation (2012, background): “Further results for related problems may be found in [1, 7, 8, 18, 22, 25, 26] and the references therein.”
Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms (2006, background): “Let I = [0, 1] and S+ , Q be the sets given by Lemmas 3.”
Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ (2016, unknown): “R−r vn 2γt t−1 it−1 t . 30 Now, following the same iteration arguments explored in [4], we ﬁnd |vn|L∞(|x|≥R) ≤ C|vn|p(|x|≥R/2). (4.6) BD1 For x0 ∈ BR, we can use the same argument taking η ∈ C∞ 0 (R2,[0,1]) with η(x) = 1 if |x−x0| ≤ ρ′ and η(x) = 0 if |x −x0| > 2ρ′ and |∇η| ≤ 2 ρ′ , to prove that”
On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents (2016, background): “and asymptotic behavior of the solutions of the Choquard equations under diﬀerent assumptions of the potentials and the nonlinearities attract a lot of attention and interest. We refer the readers to [1, 10] for the strongly indeﬁnite case with sign-changing periodic potential V, where the existence”
Periodic Nonlinear Schrödinger Equation with Application to Photonic Crystals (2004, result): “See also [1, 4, 5, 15, 11, 19, 39] for some other results on NLS.”