Results 31 to 40 of about 740 (152)
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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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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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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Existence of solutions for singular double phase problems via the Nehari manifold method [PDF]
, 2022 In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has the combined effect of a singular and of a parametric term.
Papageorgiou, Nikolaos S. +3 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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THE NEHARI MANIFOLD FOR A ψ-HILFER FRACTIONAL p-LAPLACIAN
, 2020 In this paper, we discuss the existence and non-existence of weak solutions to the non-linear problem with a fractional p-Laplacian introduced by the ψ-Hilfer fractional operator, by combining the technique of Nehari manifolds and fibering maps. Also, we
O'Regan, Donal +2 more
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Nehari manifold approach for superlinear double phase problems with variable exponents
, 2023 In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby
Crespo-Blanco, Ángel, Winkert, Patrick
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain Rx×TLy$\mathbb {R}_x \times \mathbb {T}_{L_y}$. This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated.
Christian Klein, Christof Sparber
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we investigate the dynamics of higher‐order solutions for a class of damped wave equations posed in Rn and driven by a nonlocal cubic convolution source of Hartree type. The model incorporates a higher order Laplacian of order σ, spatially dependent density functions, and frictional damping mechanisms.
Khaled Zennir +4 more
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