Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs [PDF]
SIAM Journal on Scientific ComputingA Nehari manifold optimization method (NMOM) is introduced for finding 1-saddles, i.e., saddle points with the Morse index equal to one, of a generic nonlinear functional in Hilbert spaces. Actually, it is based on the variational characterization that 1-
Zhaoxing Chen +3 more
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The Nehari manifold for elliptic equation involving the square root of the Laplacian
Journal of Differential Equations, 2011 AbstractIn this paper, we introduce the Nehari manifold for elliptic problems involving the square root of the Laplacian. We use it to establish the existence of solutions and multiple solutions for some nonlinear elliptic problem with sign-changing weight. We also establish some bifurcation results and non-existence results.
Xiaohui Yu
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Existence and multiplicity for fractional Dirichlet problem with $γ(ξ)$-Laplacian equation and Nehari manifold [PDF]
Applicable Analysis and Discrete Mathematics, 2023 This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem ...
J. Vanterler da C. Sousa +2 more
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The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function
Journal of Differential Equations, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K.J. Brown, Yanping Zhang
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The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition
Journal of Mathematical Analysis and Applications, 2012 Abstract Using the Nehari manifold and fibering maps, we prove the existence theorem of the nonlinear boundary problem − Δ u + u = | u | p − 2 u for x ∈ Ω ; ∂ u ∂ n = λ | u | q − 2 u for x ∈ ∂ Ω on a bounded domain Ω ⊆ R N .
Jinguo Zhang, Xiaochun Liu
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The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator [PDF]
Fractional Differential Calculus, 2016 Abdeljab ar Ghanmi, Kamel Saoudi
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Nehari manifold approach for a singular multi-phase variable exponent problem [PDF]
This paper is concerned with a singular multi-phase problem with variable singularities. The main tool used is the Nehari manifold approach. Existence of at least two positive solutions with positive-negative energy levels are obtained.
Mustafa Avcı
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The Nehari manifold for systems of nonlinear elliptic equations [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2006 Abstract This paper deals with the existence and multiplicity results of nonlocal positive solutions to the following system: - Δ p u = λ | u | p 1 - 2 u + ( α + 1 ) u | u | α - 1 | v | β + 1 , - Δ q v = μ | v | q - 2 v + ( β + 1 ) | u |
Khalid Adriouch, A. El Hamidi
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Ground State Solutions of Schrödinger‐Kirchhoff Equations with Potentials Vanishing at Infinity
Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 In this paper, we deal with the following Schrödinger‐Kirchhoff equation with potentials vanishing at infinity: −ε2a+εb∫ℝ3∇u2Δu+Vxu=Kxup−1u in ℝ3and u > 0, u ∈ H1(ℝ3), where V(x) ~ |x|−α and K(x) ~ |x|−β with 0 < α < 2, and β > 0. We first prove the existence of positive ground state solutions uε ∈ H1(ℝ3) under the assumption that σ < p < 5 for some σ =
Dongdong Sun, Baowei Feng
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