Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established.
Huixing Zhang
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Existence of Solutions for Nonhomogeneous Choquard Equations Involving p-Laplacian
Mathematics, 2019 This paper is devoted to investigating a class of nonhomogeneous Choquard equations with perturbation involving p-Laplacian. Under suitable hypotheses about the perturbation term, the existence of at least two nontrivial solutions for the given problems ...
Xiaoyan Shi, Yulin Zhao, Haibo Chen
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On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient [PDF]
Topological Methods in Nonlinear Analysis, 2017 We study applicability conditions of the Nehari manifold method for the equation of the form $ D_u T(u)- D_u F(u)=0 $ in a Banach space $W$, where $ $ is a real parameter. Our study is based on the development of the theory Rayleigh's quotient for nonlinear problems.
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Multiplicity of Positive Solutions of laplacian systems with sign-changing weight functions
Sahand Communications in Mathematical Analysis, 2014 In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
Seyyed Sadegh Kazemipoor +1 more
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Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping
Journal of Function Spaces, 2015 This paper is concerned with the nonlinear Schrödinger lattice with nonlinear hopping. Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state.
Ming Cheng
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Existence and multiplicity of positive solutions for indefinite semilinear elliptic problems in R^N
Electronic Journal of Differential Equations, 2014 In this article, we study a class of indefinite semilinear elliptic problems in R^N. By using the fibering maps and studying some properties of the Nehari manifold, we obtain the existence and multiplicity of positive solutions.
Yi-Hsin Cheng, Tsung-Fang Wu
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The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities
Communications on Pure & Applied Analysis, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Singular elliptic systems involving concave terms and critical Caffarelli-Kohn-Nirenberg exponents
Electronic Journal of Differential Equations, 2012 In this article, we establish the existence of at least four solutions to a singular system with a concave term, a critical Caffarelli-Kohn-Nirenberg exponent, and sign-changing weight functions. Our main tools are the Nehari manifold and the mountain
Mohammed E. O. El Mokhtar
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Homoclinic Solutions for a Class of Nonlinear Difference Equations
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach.
Ali Mai, Zhan Zhou
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A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent
, 2019 Let $(M,\textit{g},\sigma)$ be a compact Riemannian spin manifold of dimension $m\geq2$, let $\mathbb{S}(M)$ denote the spinor bundle on $M$, and let $D$ be the Atiyah-Singer Dirac operator acting on spinors $\psi:M\to\mathbb{S}(M)$.
Bartsch, Thomas, Xu, Tian
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