Results 21 to 30 of about 351 (124)
The Nehari manifold for a degenerate logistic parabolic equation
, 2023 The present paper analyses the behavior of solutions to a degenerate logistic equation with a nonlinear term of the form b(x)f(u), where the weight function b is assumed to be nonpositive. We exploit variational techniques and comparison principle in order to study the evolutionary dynamics.
Fernandes, Juliana, Maia, Liliane A.
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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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A geometrical view of the Nehari manifold [PDF]
Methods and Applications of Analysis, 2012 We study the Nehari manifold N associated to the boundary value problem −∆u = f(u) , u ∈ H 0 (Ω) , where Ω is a bounded regular domain in Rn. Using elementary tools from Differential Geometry, we provide a local description of N as an hypersurface of the Sobolev space H1 0 (Ω). We prove that, at any point u ∈ N , there exists an exterior tangent sphere
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Ground State Solutions for a Nonlocal System in Fractional Orlicz-Sobolev Spaces
International Journal of Differential Equations, 2022 We consider an elliptic system driven by the fractional a.-Laplacian operator, with Dirichlet boundary conditions type. By using the Nehari manifold approach, we get a nontrivial ground state solution on fractional Orlicz–Sobolev spaces.
Hamza El-Houari +2 more
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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)&=λf(x)|u|^{q-2}u+ \frac{2α}{α+β}\left|u\right|^{α-2}u|v|^β& \text{in } Ω,\\ \mc L_M(v)&=μg(x)|v|^{q-2}v+ \frac{2β}{α+β}\left|u\right|^α|v|^{β-2}v & \text{in }
do Ó, J. M. +2 more
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On a class of nonlocal nonlinear Schrödinger equations with potential well
Advances in Nonlinear Analysis, 2019 In this paper we investigate the existence, multiplicity and asymptotic behavior of positive solution for the nonlocal nonlinear Schrödinger equations. We exploiting the relationship between the Nehari manifold and eigenvalue problems to discuss how the ...
Wu Tsung-fang
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Existence of Weak Solutions for Nonlinear Time-Fractional p-Laplace Problems
Journal of Applied Mathematics, 2014 The existence of weak solution for p-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the ...
Meilan Qiu, Liquan Mei
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Blow up results for a viscoelastic Kirchhoff-type equation with logarithmic nonlinearity and strong damping [PDF]
Mathematica Moravica, 2021 A Kirchhoff equation type with memory term competing with a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for the initial data in a stability set created from Nehari Manifold and prove blow
Ferreira Jorge +3 more
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The Nehari manifold approach for singular equations involving the p(x)-Laplace operator [PDF]
Complex Variables and Elliptic Equations, 2021 We study the following singular problem involving the p$(x)$-Laplace operator $Δ_{p(x)}u= div(|\nabla u|^{p(x)-2}\nabla u)$, where $p(x)$ is a nonconstant continuous function, \begin{equation} \nonumber {(\rm P_λ)} \left\{\begin{aligned} - Δ_{p(x)} u & = a(x)|u|^{q(x)-2}u(x)+ \frac{λb(x)}{u^{δ(x)}} \quad\mbox{in}\,Ω,\\ u &>0 \quad\mbox{in ...
Dušan D. Repovš, Kamel Saoudi
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent
Journal of Function Spaces, 2022 In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
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