Results 41 to 50 of about 89 (80)

Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when α\alpha is close to 2

Advances in Nonlinear Analysis
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-\Delta u+u=\left({{\rm{I}}}_{\alpha }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{\alpha } is the Riesz potential and α\alpha is sufficiently ...
Luo Huxiao, Zhang Dingliang, Xu Yating
doaj   +1 more source

Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates

Advanced Nonlinear Studies, 2020
We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained ...
Mancini Gabriele, Martinazzi Luca
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Dirac-harmonic maps with potential. [PDF]

Lett Math Phys, 2022
Branding V.
europepmc   +1 more source

Normalized solutions for the Choquard equation with potential and combined nonlinearities

Advances in Nonlinear Analysis
In this paper, we study multiple normalized solutions for the following Choquard equation:
Xing Wenjun, Suo Hongmin, Lei Chunyu
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Compactness results for prescribed Webster scalar curvature problem on CR sphere

Advances in Nonlinear Analysis
In this paper we prove some results on the compactness of solutions to the prescribed Webster scalar curvature problem on S3,θ0 $\left({\mathbb{S}}^{3},{\theta }_{0}\right)$ . We first combine blow-up analysis with the subcritical approximation method to
Li Yan, Tang Zhongwei, Zhou Ning
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Nonexistence of positive radial solutions for a problem with singular potential

Advances in Nonlinear Analysis, 2014
This article completes the picture in the study of positive radial solutions in the function space 𝒟1,2(ℝN)∩L2(ℝN,|x|-αdx)∩Lp(ℝN)${{\mathcal {D}^{1,2}({\mathbb {R}^N}) \cap L^2({{\mathbb {R}^N}, | x |^{-\alpha } dx})\cap L^p({\mathbb {R}^N})}}$ for the ...
Catrina Florin
doaj   +1 more source

Nonlinear elliptic equations with self-adjoint integro-differential operators and measure data under sign condition on the nonlinearity

Advanced Nonlinear Studies
We study the existence problem for semilinear equations (E): −Au = f(⋅, u) + μ, with Borel measure μ and operator A that generates a symmetric Markov semigroup.
Klimsiak Tomasz
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Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

Advances in Nonlinear Analysis, 2018
Consider nonlinear Choquard ...
Seok Jinmyoung
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Blow-up solutions to the Hartree-Fock type Schrödinger equation with the critical rotational speed

Advances in Nonlinear Analysis
In this article, we are concerned with the existence, non-existence, and blow-up behavior of normalized ground state solutions for the mass critical Hartree-Fock type Schrödinger equation with rotation i∂tu=−Δu+2V(x)u+2ΩLzu−λu−bu∫RN∣u(y)∣2∣x−y∣2dy,(t,x ...
Tu Yuanyuan, Wang Jun
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Ground state solutions for a semilinear elliptic problem with critical-subcritical growth

Advances in Nonlinear Analysis, 2018
We prove the existence of at least one ground state solution for the semilinear elliptic ...
Alves Claudianor O., Ercole Grey, Huamán Bolaños M. Daniel   +2 more
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