The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function

By K. J. Brown, Yanping Zhang. 2003

432 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b6912cfdbf68b905c74cad47e4746b2bce7a98b

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

The Nehari manifold for fractional systems involving critical nonlinearities (2015, methodology): “1 [22] X. Shang, J. Zhang, Y. Yang, Positive solutions of nonhomogeneous fractional Laplacian problem with critical exponent, Comm. Pure Appl.”
The Nehari manifold for systems of nonlinear elliptic equations (2006, neutral): “An interesting and useful characterization of N , [15, 18, 22, 10, 7] is the following N = {(su, tv) / (s, u, t, v) ∈ Z∗ and ∂sI(su, tv) = ∂tI(su, tv) = 0}, where Z∗ = (R\{0})×(W 1,p Γ1 (Ω)\{0})×(R\{0})×(W 1,q Γ2 (Ω)\{0}) and I is considered as a functional of four variables (s, u, t, v) in Z := R ×”
Nehari manifold and existence of positive solutions to a class of quasilinear problems (2005, background): “Zhang [6] have studied a subcritical semilinear elliptic equation with a sign-changing weight function and a bifurcation real parameter in the case p = 2 and Dirichlet boundary conditions.”
An exact estimate result for a class of singular equations with critical exponents (2011, background): “In Section 2 we obtain the value Λ through the connection between Nλ and the fibrering maps (i.e., maps of the form t → Iλ(tu); see Alves and El Hamidi [1], Brown and Zhang [7]).”
Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function (2009, background): “Among the other interesting problems which are similar of equation (Ea;b) for q = 1, Brown-Zhang [ 2 ] have investigated the following equation: ‰ i¢u = ‚a(x)u + b(x)jujpi1 u in ›;”
A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function (2008, methodology): “In this paper, we give a very simple variational method which is similar to the “fibering method” of Pohozaev’s (see [3] or [4]) to prove the existence of at least two nontrivial nonnegative solutions of problem (Eλ,μ).”
The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions (2011, methodology): “(2.4) Furthermore, similar to the argument in Brown-Zhang [9, Theorem 2.3] (or see BindingDrábek-Huang [6]), we can conclude the following result.”
A fibering map approach to a potential operator equation and its applications (2009, methodology): “Such maps are known as fibering maps and were introduced by Drabek-Pohozaev in [10] and are also discussed in Brown-Zhang [8].”