Results 81 to 90 of about 52,371 (280)
Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent
, 2016 In this paper, we establish the existence of ground state solutions for fractional Schrodinger equations with a critical exponent. The methods used here are based on the $s-$harmonic extension technique of Caffarelli and Silvestre, the concentration ...
K. Teng, Xiumei He
semanticscholar +1 more source
Communications on Pure and Applied Analysis, 2019 In this paper, we study the following fractional Kirchhoff equation with critical nonlinearity \begin{document}$ \Big(a+b\int_{\mathbb{R}^3}| (-\Delta)^{\frac{s}{2}} u|^2dx\Big) (-\Delta )^su+V(x) u = K(x)|u|^{2_s^*-2}u+\lambda g(x,u), \; \text{in ...
Guangze Gu, Xianhua Tang, Youpei Zhang
semanticscholar +1 more source
Variations in Hawaiian Plume Flux Controlled by Ancient Mantle Depletion
AGU Advances, Volume 6, Issue 2, April 2025.Abstract Mantle plumes—upwellings of buoyant rock in Earth's mantle—feed hotspot volcanoes such as Hawai‘i. The size of volcanoes along the Hawai‘i–Emperor chain, and thus the magma flux of the Hawaiian plume, has varied over the past 85 million years. Fifteen and two million years ago, rapid bursts in magmatic production led to the emergence of large ...
Paul Béguelin +5 more
wiley +1 more source
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
core +3 more sources
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
doaj +1 more source
Minimizers and symmetric minimizers for problems with critical Sobolev exponent
Topological Methods in Nonlinear Analysis, 2009 In this paper we will be concerned with the existence and non-existence of constrained minimizers in Sobolev spaces $D^{k,p}({\mathbb R}^N)$, where the constraint involves the critical Sobolev exponent. Minimizing sequences are not, in general, relatively compact for the embedding $D^{k,p}({\mathbb R}^N)\hookrightarrow L^{p^*} ({\mathbb R}^N,Q ...
openaire +5 more sources
Investigating the Lid Effect on the Generation of Ocean Island Basalts: 2. Geodynamical Simulations
Geochemistry, Geophysics, Geosystems, Volume 26, Issue 4, April 2025.Abstract The concept that oceanic lithosphere mechanically limits upwelling and decompression melting of mantle plumes is known as the lid effect and is backed up by observations of ocean island basalt (OIB) geochemistry. Nevertheless, in a recent companion study on OIB geochemistry, several additional factors were identified that further influence OIB
Shihao Jiang +5 more
wiley +1 more source
A Liouville theorem for ancient solutions to a semilinear heat equation and its elliptic counterpart
, 2020 We establish the nonexistence of nontrivial ancient solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$ which are smaller in absolute value than the self-similar radial singular steady state, provided that the exponent $p$ is strictly ...
Sourdis, Christos
core
On Schrödinger equation with periodic potential and critical Sobolev exponent
Topological Methods in Nonlinear Analysis, 1998 The main purpose of this paper is to establish the existence of a solution of the semilinear Schr¨odinger equation (1) −u + V (x)u = K(x)|u|2−2u + f(x, u) in RN, involving a critical Sobolev exponent 2 = 2N/(N − 2) with N 4 and a subcritical nonlinearity f : RN × R ! R.
Chabrowski, Jan, Yang, Jianfu
openaire +4 more sources
On the Sobolev embedding theorem for variable exponent spaces in the critical range [PDF]
Journal of Differential Equations, 2012 15 pages ...
Analía Silva +5 more
openaire +3 more sources