Semiclassical Standing Waves with Clustering Peaks for Nonlinear Schrodinger Equations

Jaeyoung Byeon, Kazunaga Tanaka (Autoren)

Buch | Softcover

89 Seiten

2014
American Mathematical Society (Verlag)
978-0-8218-9163-6 (ISBN)

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Examines the following singularly perturbed problem: - 2 ?u V(x)u=f(u) in R N . Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of V(x). A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities f .

The authors study the following singularly perturbed problem: −ϵ 2 Δu V(x)u=f(u) in R N . Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of V(x) . A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities f .

Jaeyoung Byeon, KAIST, Daejeon, Republic of Korea. Kazunaga Tanaka, Waseda University, Tokyo, Japan.

Introduction and results
Preliminaries
Local centers of mass
Neighborhood Ω ϵ (ρ,R,β) and minimization for a tail of u in Ω ϵ
A gradient estimate for the energy functional
Translation flow associated to a gradient flow of V(x) on R N
Iteration procedure for the gradient flow and the translation flow
An (N 1)ℓ 0 -dimensional initial path and an intersection result
Completion of the proof of Theorem 1.3
Proof of Proposition 8.3
Proof of Lemma 6.1
Generalization to a saddle point setting
Bibliography

Erscheint lt. Verlag	22.9.2014
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	164 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	0-8218-9163-4 / 0821891634
ISBN-13	978-0-8218-9163-6 / 9780821891636
Zustand	Neuware