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Mathematische Nachrichten, Volume 299, Issue 5, Page 1004-1027, May 2026.ABSTRACT This paper investigates the existence and non‐existence and uniqueness of global solutions for certain parameter values c$c$ in a new class of generalized fractional p$p$‐Kirchhoff equations in the whole space. Using the Pohozaev and Nehari identities for an auxiliary problem, together with the fractional Gagliardo–Nirenberg inequality and the
J. Vanterler da C. Sousa +2 more
wiley +1 more source
Electronic Journal of Differential Equations, 2018 In this article, we study the fractional elliptic equation with critical Sobolev-Hardy nonlinearity $$\displaylines{ (-\Delta)^{\alpha} u+a(x) u=\frac{|u|^{2^*_{s}-2}u}{|x|^s}+k(x)|u|^{q-2}u,\cr u\in H^\alpha(\mathbb{R}^N), }$$ where ...
Lingyu Jin, Shaomei Fang
doaj
Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent [PDF]
Communications in Contemporary Mathematics, 2015 We consider nonlinear Choquard equation [Formula: see text] where N ≥ 3, V ∈ L∞(ℝN) is an external potential and Iα(x) is the Riesz potential of order α ∈ (0, N). The power [Formula: see text] in the nonlocal part of the equation is critical with respect to the Hardy–Littlewood–Sobolev inequality.
Moroz, Vitaly, Van Schaftingen, Jean
openaire +5 more sources
Warning: Warnings Can Backfire Even When They Provide New and Important Information
Journal of Behavioral Decision Making, Volume 39, Issue 2, April 2026.ABSTRACT We clarify the conditions under which warnings that provide useful information backfire. Our analysis is based on three observations: (1) warnings can increase the attention given to the warned‐against behavior, (2) in many settings, counterproductive warned‐against behaviors (like texting while driving) are typically rewarding, and (3 ...
Ido Erev +3 more
wiley +1 more source
Toward the theory of the Sobolev classes with critical exponent
Доповiдi Нацiональної академiї наук України, 2019 It is established that an arbitrary homeomorphism f in the Sobolev class W1,n−1loc with the outer dilatation K0(x,f)∈Ln−1loc is the socalled lower Q - homeomorphism with Q=K0(x,f) and the ring Q* homeomorphism with Q∗=Kn−10(x,f).
O.S. Afanas’eva +2 more
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Function spaces for decoupling
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We introduce new function spaces LW,sq,p(Rn)$\mathcal {L}_{W,s}^{q,p}(\mathbb {R}^{n})$ that yield a natural reformulation of the ℓqLp$\ell ^{q}L^{p}$ decoupling inequalities for the sphere and the light cone. These spaces are invariant under the Euclidean half‐wave propagators, but not under all Fourier integral operators unless p=q$p=q$, in ...
Andrew Hassell +3 more
wiley +1 more source
Solutions of p(x)-Laplacian equations with critical exponent and perturbations in R^N
Electronic Journal of Differential Equations, 2012 Based on the theory of variable exponent Sobolev spaces, we study a class of $p(x)$-Laplacian equations in $mathbb{R}^{N}$ involving the critical exponent.
Xia Zhang, Yongqiang Fu
doaj
Single Blow up Solutions for a Slightly Subcritical Biharmonic Equation [PDF]
, 2004 In this paper, we consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent $(P_\epsilon): \Delta^2u=u^{9-\epsilon}, u>0$ in $\Omega$ and $u=\Delta u=0$ on $\partial\Omega$, where $\Omega$ is a smooth bounded ...
Mehdi, Khalil El
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Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we investigate the following D1,p$D^{1,p}$‐critical quasi‐linear Hénon equation involving p$p$‐Laplacian −Δpu=|x|αupα∗−1,x∈RN,$$\begin{equation*} -\Delta _p u=|x|^{\alpha }u^{p_\alpha ^*-1}, \qquad x\in \mathbb {R}^N, \end{equation*}$$where N⩾2$N\geqslant 2$, 1
Wei Dai +3 more
wiley +1 more source