Results 1 to 10 of about 93 (77)

Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities

Transactions of the London Mathematical Society, 2021
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
doaj   +2 more sources

From Hardy to Rellich inequalities on graphs

Proceedings of the London Mathematical Society, Volume 122, Issue 3, Page 458-477, March 2021., 2021
Abstract We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality.
Matthias Keller, Yehuda Pinchover, Felix Pogorzelski   +2 more
wiley   +1 more source

The existence of positive solution for an elliptic problem with critical growth and logarithmic perturbation

Advanced Nonlinear Studies, 2023
We consider the existence and nonexistence of the positive solution for the following Brézis-Nirenberg problem with logarithmic perturbation: −Δu=∣u∣2∗−2u+λu+μulogu2x∈Ω,u=0x∈∂Ω,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{ll}-\Delta u={| u| }^{{2}^
Deng Yinbin, He Qihan, Pan Yiqing, Zhong Xuexiu   +3 more
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Positive solution for a nonlocal problem with strong singular nonlinearity

Open Mathematics, 2023
In this article, we consider a nonlocal problem with a strong singular term and a general weight function. By using Ekeland’s variational principle, we prove a necessary and sufficient condition for the existence of a positive solution.
Wang Yue, Wei Wei, Xiong Zong-Hong, Yang Jian   +3 more
doaj   +1 more source

Positive solution for a class of coupled (p, q)-Laplacian nonlinear systems. [PDF]

, 2014
In this article, we prove the existence of a nontrivial positive solution for the elliptic system ⎧⎨ ⎩ –_pu = ω(x)f (v) in_, –_qv = ρ(x)g(u) in_, (u, v) = (0,0) on ∂_, where_p denotes the p-Laplacian operator, p, q > 1 and _ is a smooth bounded ...
Ferreira, Wenderson Marques, Martins, Eder Marinho   +1 more
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Thresholds for the existence of solutions to inhomogeneous elliptic equations with general exponential nonlinearity

Advances in Nonlinear Analysis, 2022
In this paper we study the existence and the nonexistence of solutions to an inhomogeneous non-linear elliptic problem (P)−Δu+u=F(u)+κμ  in  RN, u>0  in  RN, u(x)→0  as  |x|→∞,- \Delta u + u = F(u) + \kappa \mu \quad {\kern 1pt} {\rm in}{\kern 1pt ...
Ishige Kazuhiro, Okabe Shinya, Sato Tokushi   +2 more
doaj   +1 more source

Monotonicity of solutions for fractional p-equations with a gradient term

Open Mathematics, 2022
In this paper, we consider the following fractional pp-equation with a gradient term: (−Δ)psu(x)=f(x,u(x),∇u(x)).{\left(-\Delta )}_{p}^{s}u\left(x)=f\left(x,u\left(x),\nabla u\left(x)). We first prove the uniqueness and monotonicity of positive solutions
Wang Pengyan
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On the existence of positive solutions of a class of parabolic reaction diffusion systems

, 2022
In this paper, we show the existence of continuous positive solutions of a class of nonlinear parabolic reaction diffusion systems with initial conditions using techniques of functional analysis and potential analysis. Mathematics Subject Classification (
REDJOUH, Mounir, MESBAHI, Salim
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Sign changing solutions of Poisson's equation

Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020
Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
wiley   +1 more source

Positive global solutions of nonlocal boundary value problems for the nonlinear convection reaction-diffusion equations [PDF]

, 2017
In this paper, the nonlocal boundary value problems for a class of nonlinear functional convection reaction-diffusion equations with the singular reaction function are studied by using the method of upper and lower solutions and monotone iterative ...
Yan, Baoqiang, Baoqiang Yan, Ma, Tianfu, Tianfu Ma   +3 more
core   +2 more sources