Results 31 to 40 of about 521 (162)

Existence of Positive Ground State Solutions for Fractional Choquard Systems in Subcritical and Critical Cases

Mathematics, 2023
We investigate a class of fractional linearly coupled Choquard systems. For the subcritical case and all critical cases, we prove the existence, nonexistence and symmetry of positive ground state solutions of systems, by using the Nehari manifold method,
Huiqin Lu, Kexin Ouyang
doaj   +1 more source

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
wiley   +1 more source

Parametric superlinear double phase problems with singular term and critical growth on the boundary

Mathematical Methods in the Applied Sciences, Volume 45, Issue 4, Page 2276-2298, 15 March 2022., 2022
In this paper, we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth. Based on a new equivalent norm for Musielak–Orlicz Sobolev spaces and the Nehari manifold along with the fibering ...
Ángel Crespo‐Blanco, Nikolaos S. Papageorgiou, Patrick Winkert   +2 more
wiley   +1 more source

Existence of Two Solutions for a Critical Elliptic Problem with Nonlocal Term in ℝ4

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
In this paper, we prove the existence of two positive solutions for a critical elliptic problem with nonlocal term and Sobolev exponent in dimension four.
Khadidja Sabri, Atika Matallah, Safia Benmansour, Mohammed El Mokhtar Ould El Mokhtar, Pasquale Vetro   +4 more
wiley   +1 more source

Majorization Properties for Certain Subclasses of Meromorphic Function of Complex Order

Complexity, Volume 2022, Issue 1, 2022., 2022
By making use of q−differential operators, many distinct subclasses of analytic and meromorphic functions have already been defined and investigated from numerous perspectives. In this article, we investigated several majorization results for the class of meromorphic univalent functions of complex order, defined by q−differential operator. Moreover, we
Neelam Khan, Muhammad Arif, Maslina Darus, Abdellatif Ben Makhlouf   +3 more
wiley   +1 more source

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
openaire   +2 more sources

Bilateral Harnack Inequalities for Stochastic Differential Equation with Multiplicative Noise

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
By constructing a coupling with unbounded time‐dependent drift, a lower bound estimate of dimension‐free Harnack inequality with power is obtained for a large class of stochastic differential equation with multiplicative noise. The key is an application of the inverse Hölder inequality.
Zihao An, Gaofeng Zong, Salah Mahmoud Boulaaras   +2 more
wiley   +1 more source

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, Giacomoni, J., Mishra, P. K.   +2 more
openaire   +3 more sources

Ground State Solution for a Fourth Order Elliptic Equation of Kirchhoff Type with Critical Growth in ℝN

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
wiley   +1 more source