In this paper, we study the following nonlinear fractional Schr\documentclass[12pt]{minimal}\begin{document}$\ddot{\mbox{o}}$\end{document}ödinger equation with critical exponent \documentclass[12pt]{minimal}\begin{document}$h^{2\alpha }(-\Delta )^{\alpha }u + V(x)u= |u|^{2_{\alpha }^{*}-2}u \lambda |u|^{q-2}u, x\in \mathbb {R}^{N}$\end{document}h2α(−Δ)αu+V(x)u=|u|2α*−2u+λ|u|q−2u,x∈RN, where h is a small positive parameter, 0 < α 1,...

Membrane-associated RING-CH8 (MARCH8) is a member of the recently discovered MARCH family ubiquitin ligases. MARCH8 has been shown to participate in immune responses. However, role prognosis and immunology human cancers remains largely unknown. The expression protein was detected via immunohistochemistry non-small cell lung cancer (NSCLC) non-cancerous tissues. study investigated tumor immunity through pan-cancer analysis multiple databases. genetic alternations were explored with...

The purposes of the present study are to investigate effects reduced muscle loading by prolonged immobilization on regeneration fibrocartilaginous enthesis through endochondral ossification in rabbits. Forty-eight rabbits underwent standard partial patellectomy were randomly divided into control group and (PIM) group. immobilized cast was only maintained for first 4 weeks group, while 12 or until euthanization PIM Patella-patella tendon complexes harvested Micro-CT histology at week 6, 18....

We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ velocity with flexible size. DEDF is obtained by $\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$, where $\mathbf{M}$ set moment Maxwellian function, $\mathbf{C}$ matrix connecting moments. numerical components are determined model. calculation $\mathbf{C}^{-1}$ based...

In this paper, we study the following problem\begin{eqnarray} (-\Delta)^{\frac{\alpha}{2}}u = K(x)|u|^{2_{\alpha}^{*}-2}u + f(x) \quad in \ \Omega,\\ u=0 on \partial \Omega,\end{eqnarray}where $\Omega\subset R^N$ is a smooth bounded domain, $0\alpha$, $ 2_{\alpha}^{*}= \frac{2N}{N-\alpha}$, $f\inH^{-\frac{\alpha}{2}}(\Omega)$ and $K(x)\in L^\infty(\Omega)$.Under appropriate assumptions $K$ $f$, prove that thisproblem has at least two positive solutions. When $\alpha 1$, wealso establish...

Abstract We study the Dancer–Fučík spectrum of fractional p -Laplacian operator. construct an unbounded sequence decreasing curves in using a suitable minimax scheme. For = 2, we present very accurate local analysis. minimal and maximal locally near points where it intersects main diagonal plane. give sufficient condition for region between them to be nonempty show that is free case simple eigenvalue. Finally, compute critical groups various regions separated by these curves. precisely...

We obtain a Struwe type global compactness result for class of nonlinear nonlocal problems involving the fractional $p-$Laplacian operator and nonlinearities at critical growth.

We prove existence and multiplicity results for a $N$-Laplacian problem with critical exponential nonlinearity that is natural analog of the Brezis-Nirenberg borderline case Sobolev inequality. This extends in literature semilinear $N = 2$ to all \ge 2$. When > nonlinear operator $- \Delta_N$ has no linear eigenspaces hence this extension requires new abstract point theorems are not based on subspaces. ${\mathbb Z}_2$-cohomological index related pseudo-index applicable here.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 3 April 2020Accepted: 07 December 2020Published online: 16 February 2021Keywordsinverse problems, nonlinearity, Boltzmann equation, collision operatorAMS Subject Headings35R30, 35Q20Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher: Society for Industrial and Applied MathematicsCODEN: sjmaah

We prove a bifurcation and multiplicity result that is independent of the dimension N for critical p-Laplacian problem analog Brezis-Nirenberg quasilinear case. This extends in literature semilinear case p = 2 to all (1;infty). In particular, it gives new existence when \le p^2. When \neq nonlinear operator -\Delta_p has no linear eigenspaces, so our extension nontrivial requires abstract point theorem not based on subspaces. pseudoindex related Z^2-cohomological index applicable here.

Abstract We construct nonlinear entire anisotropic minimal graphs over $\mathbb{R}^{4}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:math> , completing the solution to Bernstein problem. The examples we have a variety of growth rates, and our approach both generalizes higher dimensions recovers elucidates known $\mathbb{R}^{n},\, n \geq 8$ <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mo>≥</mml:mo>...

Transposed Poisson structures on the Schr\"{o}dinger algebra in $(n+1)$-dimensional space-time of Lie groups are described. It was proven that $\mathcal{S}_{n}$ case $n\neq 2$ does not have non-trivial $\frac{1}{2}$-derivations and as it follows admit transposed structures. All for $\mathcal{S}_{2}$ obtained. Also, we proved admits a ${\rm Hom}$-Lie structure.