New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation
By Xianhua Tang. 2014
106 citations recorded by the source corpus.
Abstract Consider the semilinear Schrödinger equation where f is a superlinear, subcritical nonlinearity. We mainly study the case where both V and f are periodic in x and 0 belongs to a spectral gap of −Δ + V. Based on the work of Szulkin and Weth [J Funct Anal 257: 3802-3822, 2009], we develop a new technique to show the boundedness of Cerami sequences and derive a new super-quadratic condition that there exists a θ0 ∈ (0, 1) such that for the existence a “ground state solution” which minimizes the corresponding energy among all nontrivial solutions. Our result unifies and improves some known ones and the recent ones of Szulkin and Weth [J Funct Anal 257: 3802-3822, 2009] and Liu [Calc. Var. 45: 1-9, 2012].
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/9447b9371b60183d5b63a038d083a9513d73ef87
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Non-Nehari manifold method for asymptotically periodic Schrödinger equations (2014, background): “1) after Szulkin and Weth [25] in which, various conditions better than (Ne) are obtained, see [18, 23, 27, 33].”
- NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION (2014, background): “On the existence of this kind “ground state solutions”, a weaker condition was obtained in very recent paper [24].”
- New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, methodology): “More general conditions on f were obtained in Ding and Lee [9], Liu [19], Szulkin and Weth [27], Tang [29] and the references therein.”