The method of Nehari manifold

By A. Szulkin, Tobias Weth. 2010

410 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/40fba30d9c1fb894897862efec5d8eacc3918134

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Citations in the corpus

Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent (2017, methodology): “Here we have taken advantage of the monotonicity of the perturbation, thus the Nehari manifold method works, for the detail proofs, we refer to [31,36].”
Multiplicity and concentration of solutions to the nonlinear magnetic Schrödinger equation (2020, background): “1 and the abstract category theorem [35], ε has at least catπ (M)(π (M)) critical points on S+ ε .”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “We refer to the book chapter of Szulkin-Weth [44] which describes the method very well.”
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”
Existence and concentration of positive solutions for semilinear Schrödinger–Poisson systems in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin} (2012, unknown): “3 of [29]) Under the assumptions of Lemma 2.”
Solutions to overdetermined elliptic problems in nontrivial exterior domains (2016, background): “It is well known that, I(un) = inf{max{I(tu) : t > 0} , u ∈ H 1 0,r(B c Rn)} > 0, see for instance [29].”
Fractional double-phase patterns: concentration and multiplicity of solutions (2020, methodology): “This difficulty will be overcome by using some abstract critical point results obtained in [68].”
Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method (2013, methodology): “By using (M1)–(M3) we have, as in [26], the following variational characterization of the infimum of Jε over Nε: cε = inf u∈Nε Jε(u) = inf u∈H ε max t>0 Jε(tu) = inf u∈S ε max t>0 Jε(tu).”
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].”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, methodology): “We mention the book chapter of Szulkin-Weth [46] in order to have a very well description of the method.”