Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems

By A. Szulkin, Wenming Zou. 2001

167 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f6696ad2675539f9ea7521a62608348aed6cce56

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Superlinear problems without Ambrosetti and Rabinowitz growth condition (2008, background): “Then several researchers studied problem (P ) trying to drop the above condition (f ′ 3), see for instance, [3,7,10].”
A positive solution for a nonlinear Schrödinger equation on Rn (2005, background): “We mention, for example, [ 10 ] for a linking type situation.”
NON-NEHARI-MANIFOLD METHOD FOR ASYMPTOTICALLY LINEAR SCHRÖDINGER EQUATION (2014, background): “Then, for any e ∈ E + 0 , sup Φ ( E − ⊕ R + e ) < ∞ and there is R e > 0 such that This result is essentially contained in [11], see also [7, Lemma 3.1], but for the reader’s convenience we choose to write it in detail.”
On a semilinear Schrodinger equation with critical Sobolev exponent (2001, unknown): “[1, 3, 5, 9, 11, 13, 16 , 17, 18] and the references there.”
Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential (2009, background): “Here we only mention [1–15].”
Homoclinic orbits for a nonperiodic Hamiltonian system (2007, background): “See also [19] for a periodic setting but with different nonlinearities, in particular asymptotically linear ones.”
Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms (2006, unknown): “[21]).”
Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, methodology): “In [19, 20, 36, 42, 45], the authors used a more suitable version of the Mountain Pass Theorem to overcome this difficulty.”
A positive solution for an asymptotically linear elliptic problem on$\mathbb{R}^N$ autonomous at infinity (2002, background): “Finally we wish to mention [ 13 ] where a rst order Hamiltonian system with an asymptotically linear part is studied.”
WEAK LINKING THEOREMS AND SCHR¨ ODINGER EQUATIONS WITH CRITICAL SOBOLEV EXPONENT (2003, unknown): “Noting that un := un + u + n |·|w → u implies that un ⇀ u weakly in E and un → u strongly in E, then the proof is the same as that in [23] (see also [6, 12]).”
Solutions for Discrete Periodic Schrödinger Equations with Spectrum 0 (2010, methodology): “In [21, 24 , 28], the authors developed monotonicity trick for strongly indefinite problem which is mainly due to Jeanjean [13] for studying Landesman-Lazer type problems in R N .”