Results 21 to 30 of about 447 (79)
Advanced Nonlinear Studies, 2023 In our previous paper [K. Ishige, S. Okabe, and T. Sato, A supercritical scalar field equation with a forcing term, J. Math. Pures Appl. 128 (2019), pp.
Ishige Kazuhiro +2 more
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Shooting with degree theory: Analysis of some weighted poly-harmonic systems [PDF]
, 2014 In this paper, the author establishes the existence of positive entire solutions to a general class of semilinear poly-harmonic systems, which includes equations and systems of the weighted Hardy--Littlewood--Sobolev type.
Villavert, John
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Existence of groundstates for a class of nonlinear Choquard equations [PDF]
, 2012 We prove the existence of a nontrivial solution (u \in H^1 (\R^N)) to the nonlinear Choquard equation [- \Delta u + u = \bigl(I_\alpha \ast F (u)\bigr) F' (u) \quad \text{in (\R^N),}] where (I_\alpha) is a Riesz potential, under almost necessary ...
Jean, Van Schaftingen, Vitaly Moroz
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A system of equations involving the fractional p-Laplacian and doubly critical nonlinearities
Advanced Nonlinear Studies, 2023 This article deals with existence of solutions to the following fractional pp-Laplacian system of equations: (−Δp)su=∣u∣ps*−2u+γαps*∣u∣α−2u∣v∣βinΩ,(−Δp)sv=∣v∣ps*−2v+γβps*∣v∣β−2v∣u∣αinΩ,\left\{\begin{array}{l}{\left(-{\Delta }_{p})}^{s}u={| u| }^{{p}_{s}^{
Bhakta Mousomi +2 more
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Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit [PDF]
, 2015 In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume ...
Khoa, Vo Anh, Muntean, Adrian
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Multiple positive solutions to elliptic boundary blow-up problems [PDF]
, 2016 We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem \[ \left\{\begin{array}{ll} \Delta u + \bigl(a^+(\vert x \vert) - \mu a^-(\vert x \vert)\bigr) g(u) = 0, & \; \vert x \vert < 1, \\ u(x)
Aftalion +44 more
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Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity [PDF]
, 2014 This paper deals with the existence and the asymptotic behavior of non-negative solutions for a class of stationary Kirchhoff problems driven by a fractional integro-differential operator $\mathcal L_K$ and involving a critical nonlinearity.
Autuori, Giuseppina +2 more
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(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group
Open Mathematics, 2020 The paper deals with the existence of solutions for (p,Q)(p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin.
Pucci Patrizia, Temperini Letizia
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Symmetric results of a Hénon-type elliptic system with coupled linear part
Open Mathematics, 2022 In this article, we study the elliptic system: −Δu+μ1u=∣x∣αu3+λv,x∈Ω−Δv+μ2v=∣x∣αv3+λu,x∈Ωu,v>0,x∈Ω,u=v=0,x∈∂Ω,\left\{\begin{array}{ll}-\Delta u+{\mu }_{1}u=| x\hspace{-0.25em}{| }^{\alpha }{u}^{3}+\lambda v,& x\in \Omega \\ -\Delta v+{\mu }_{2}v=| x ...
Lou Zhenluo, Li Huimin, Zhang Ping
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