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Non-Nehari manifold method for a semilinear Schrödinger equation with critical Sobolev exponent
, 2016 Huxiao Luo +3 more
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Transversality of stable and Nehari manifolds for a semilinear heat equation [PDF]
Calculus of Variations and Partial Differential Equations, 2011 It is well known that for the subcritical semilinear heat equation, negative initial energy is a sufficient condition for finite time blowup of the solution. We show that this is no longer true when the energy functional is replaced with the Nehari functional, thus answering negatively a question left open by Gazzola and Weth (2005). Our proof proceeds
Flávio Dickstein +3 more
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Infinite Sharp Conditions by Nehari Manifolds for Nonlinear Schrödinger Equations
The Journal of Geometric Analysis, 2019We study the Cauchy problem of nonlinear Schrodinger equation $$i\varphi _t+\Delta \varphi +|\varphi |^{p-1}\varphi =0$$. By constructing infinite Nehari manifolds with geometric features, we not only obtain infinite invariant sets of solutions, but also give infinite sharp conditions for global existence and finite time blow up of solutions.
Wei Lian +3 more
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A minimization problem with variable growth on Nehari manifold
Monatshefte für Mathematik, 2016In this paper, based on the theory of variable exponent space, we study a class of minimizing problem on Nehari manifold via concentration compactness principle. Under suitable assumptions, by showing a relative compactness of minimizing sequences, we prove the existence of minimizers.
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Nehari manifold and existence of positive solutions to a class of quasilinear problems
Nonlinear Analysis: Theory, Methods & Applications, 2005Abstract In this paper, existence and multiplicity results to the following nonlinear elliptic equation: - Δ p u = λ | u | q - 2 u + | u | p * - 2 u , u > 0 in Ω ⊂ R N , together with mixed Dirichlet–Neumann or Neumann boundary conditions, are established. Here, Δ p
A. El Hamidi, Claudianor O. Alves
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The Nehari manifold and application to a semilinear elliptic system
Nonlinear Analysis: Theory, Methods & Applications, 2009Abstract In this paper, we study the Nehari manifold and its application to the following semilinear elliptic system: { − Δ u + u = λ f ( x ) | u | q − 2 u , x ∈ Ω , − Δ v + v = μ g ( x ) | v | q − 2 v , x ∈ Ω , ∂ u ∂ n = α α + β h ( x )
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Ground state and multiple solutions via generalized Nehari manifold
Nonlinear Analysis: Theory, Methods & Applications, 2014Abstract By using variational methods and the generalized Nehari manifold due to Szulkin and Weth, the existence of the ground states and the multiplicity of solutions for a wide class of superlinear elliptic equations is studied.
X. Zhong, Wenming Zou
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