EXISTENCE AND CONCENTRATION BEHAVIOR OF NODE SOLUTIONS FOR A KIRCHHOFF EQUATION IN R~3

By Yanke Peng. 2015

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Concentrating Bound States for Kirchhoff Type Problems in ℝ3 Involving Critical Sobolev Exponents (2013, methodology): “5) Unlike [13] and [30], where the minimum of V (x) is global and the mountain-pass lemma can be used globally, here in the present paper, the condition (V2) is local, hence we need to use a local mountain-pass argument introduced in [23], which also helps us to overcome the obstacle caused by the n”
Existence of positive solutions to Kirchhoff type problems with zero mass (2014, unknown): “…on f is often assumed: (f) f (t)t 4F (t) for |t| large, where F (t) = ∫ t0 f (s)ds, ✩ Partially supported by National Natural Science Foundation of China (Grant No. 11071149, 11301313), and Science Council of Shanxi Province (2010011001-1, 2012011004-2, 2013021001-4) and Shanxi 100 Talent program.”