Ground state solutions for some indefinite variational problems

By A. Szulkin, Tobias Weth. 2009

531 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/da3d25fca02ea006f5049fdb281c91d3c6e5aa1d

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

NON-NEHARI-MANIFOLD METHOD FOR ASYMPTOTICALLY LINEAR SCHRÖDINGER EQUATION (2014, methodology): “In [10], based on the Nehari-manifold method, Szulkin and Weth developed an approach to find ground state solutions of Nehari–Pankov type for problem (1.”
The method of Nehari manifold (2010, methodology): “In [44] it has been shown that (22) has a ground”
NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION (2014, methodology): “To state the results obtained by Szukin and Weth in [21, 22], we first introduce the following assumptions: (F1) f ∈ C(Ω × R, R), and there exist constants p ∈ (2, 2∗) and C0 > 0 such that |f(x, t)| ≤ C0 ( 1 + |t|p−1) , ∀ (x, t) ∈ Ω× R; (F2) f(x, t) = o(|t|), as |t| → 0, uniformly in x ∈ Ω; (SQ) lim”
Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method (2013, methodology): “6) has multiple positive solutions when λ is large enough, by using Lusternik–Schnirelmann theory, minimax methods and a approach as in [26] (see also [25]).”
A mass supercritical problem revisited (2020, methodology): “However, since F̃ is not required to be of class C, we need to adapt their argument by making use of techniques due to Szulkin and Weth [43, 44].”
New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, background): “There is a large literature on existence and multiplicity results, for example, [3,5–7,9–11,15–17,19–23,27,28,30,32,33].”
Hamiltonian elliptic systems: a guide to variational frameworks (2014, methodology): “[98] Andrzej Szulkin and Tobias Weth.”
New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation (2014, unknown): “[17] A. Szulkin, T.Weth, Ground state solutions for some indefinite variational problems, J. Funct.”
Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations (2020, background): “As in [14], [15] and [42], we choose a subset F of K such that F = −F and each orbit O(w) ⊂ K has a unique representative in F .”