Zobrazeno 1 - 10
of 353
pro vyhledávání: '"49J35"'
Autor:
Li, Jungang, Wang, Zhiwei
We study the following higher order Schr\"odinger equation on hyperbolic space $\mathbb{H}^n$: $P_m u +a(x) u = |u|^{q - 2}u,$ where $P_m$ is the $2m$ order GJMS operator, $q=\frac{2n}{n-2m}$, $a(x) \in L^{\frac{n}{2m}}(\mathbb{H}^n)$ is a nonnegativ
Externí odkaz:
http://arxiv.org/abs/2411.14719
We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by either a gra
Externí odkaz:
http://arxiv.org/abs/2411.07403
We study the following nonlinear Schr\"odinger equation and we look for normalized solutions $(u,\mu)\in H^1({\bf R}^N)\times{\bf R}$ for a given $m>0$ and $N\geq 2$ \[ -\Delta u + \mu u = g(u)\quad \text{in}\ {\bf R}^N, \qquad \frac{1}{2}\int_{{\bf
Externí odkaz:
http://arxiv.org/abs/2410.23733
In this paper, we deal with the following $(p,q)$-fractional problem $$ (-\Delta)^{s_{1}}_{p}u +(-\Delta)^{s_{2}}_{q}u=\lambda P(x)|u|^{k-2}u+\theta|u|^{p_{s_{1}}^{*}-2}u \, \mbox{ in }\, \Omega,\qquad u=0\, \mbox{ in }\, \mathbb{R}^{N} \setminus \Om
Externí odkaz:
http://arxiv.org/abs/2409.13986
Autor:
Malizia, Francesco
We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field eq
Externí odkaz:
http://arxiv.org/abs/2409.06515
Autor:
Fechner, Włodzimierz
We present two characterizations of quasiconvexity for radially semicontinuous mappings defined on a convex subset of a real linear space. As an application we obtain an extension of the Sion's minimax theorem, as well as a new characterization of qu
Externí odkaz:
http://arxiv.org/abs/2408.15983
Existence of Solutions for Fractional Optimal Control Problems with Superlinear-subcritical Controls
Autor:
Siktar, Joshua M.
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical condition. Ea
Externí odkaz:
http://arxiv.org/abs/2408.09586
Autor:
Gao, Rui, Zhu, Miaomiao
We demonstrate the existence of branched immersed 2-spheres with prescribed mean curvature, with controlled Morse index and with arbitrary codimensions in closed Riemannian manifold $N$ admitting finite fundamental group, where $\pi_k(N) \neq 0$ and
Externí odkaz:
http://arxiv.org/abs/2407.11945
Publikováno v:
Nonlinear Anal. Model. Control 29:4 (2024), 762-782
The aim of this paper is to study existence results for a singular problem involving the $p$-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is e
Externí odkaz:
http://arxiv.org/abs/2406.18982
Autor:
Gallo, Marco
In this thesis we investigate how the nonlocalities affect the study of different PDEs coming from physics, and we analyze these equations under almost optimal assumptions of the nonlinearity. In particular, we focus on the fractional Laplacian opera
Externí odkaz:
http://arxiv.org/abs/2402.08338