Results 41 to 50 of about 261,695 (153)
Nehari Manifold for Fractional Kirchhoff Systems with Critical Nonlinearity
Milan Journal of Mathematics, 2019 In this paper, we show the existence and multiplicity of positive solutions of the following fractional Kirchhoff system\\ \begin{equation} \left\{ \begin{array}{rllll} \mc L_M(u)&= f(x)|u|^{q-2}u+ \frac{2 }{ + }\left|u\right|^{ -2}u|v|^ & \text{in } ,\\ \mc L_M(v)&= g(x)|v|^{q-2}v+ \frac{2 }{ + }\left|u\right|^ |v|^{ -2}v ...
Ó, J. M. do +2 more
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Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 In this paper, we consider the following fourth order elliptic Kirchhoff‐type equation involving the critical growth of the form Δ2u−a+b∫ℝN∇u2dxΔu+Vxu=Iα∗Fufu+λu2∗∗−2u,in ℝN,u∈H2ℝN, where a > 0, b ≥ 0, λ is a positive parameter, α ∈ (N − 2, N), 5 ≤ N ≤ 8, V : ℝN⟶ℝ is a potential function, and Iα is a Riesz potential of order α.
Li Zhou, Chuanxi Zhu, Sergey Shmarev
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On p(z)–Laplacian System Involving Critical Nonlinearities
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 In this paper, we deal with the existence of at least two nonnegative nontrivial solutions to a p(z)–Laplacian system involving critical nonlinearity in the context of Sobolev spaces with variable exponents on complete manifolds. We have established our main results by exploring both Nehari’s method and doing a refined analysis on the associated fiber ...
Ahmed Aberqi +4 more
wiley +1 more source
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.
Yavdat Il’yasov
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Nehari manifold for degenerate logistic parabolic equations
Electronic Journal of Differential EquationsIn this article we analyze the behavior of solutions to a degenerate logistic equation with a nonlinear term \(b(x)f(u)\) where the weight function \(b\) is non-positive.
Juliana Fernandes, Liliane A. Maia
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Nodal solutions for the Choquard equation [PDF]
, 2016 We consider the general Choquard equations $$ -\Delta u + u = (I_\alpha \ast |u|^p) |u|^{p - 2} u $$ where $I_\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + \alpha}{N}, \frac{N + \alpha}{N - 2})$ and ...
Ghimenti, Marco, Van Schaftingen, Jean
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, 2017 We study a $p$-Laplacian equation involving a parameter $\lambda$ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari manifold and the fibering method, we show the existence of two positive solutions on some ...
Macedo, Abiel, Silva, Kaye
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Positive solutions for asymptotically linear problems in exterior domains
, 2016 The existence of a positive solution for a class of asymptotically lin- ear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter ...
Maia, Liliane A., Pellacci, Benedetta
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Ground state solution of a noncooperative elliptic system
, 2013 In this paper, we study the existence of a ground state solution, that is, a non trivial solution with least energy, of a noncooperative semilinear elliptic system on a bounded domain.
Batkam, Cyril Joel
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