Results 51 to 60 of about 1,675,583 (134)
Exact multiplicity of positive solutions to a superlinear problem
Electronic Journal of Differential Equations, 2003 We generalize previous uniqueness results on a semilinear elliptic equation with zero Dirichlet boundary condition and superlinear, subcritical nonlinearity.
Junping Shi
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Boundary Value ProblemsThis paper is concerned with the Schrödinger–Poisson–Slater equation involving the Coulomb–Sobolev exponent. We apply the concentration compactness principle and the Pohožaev-type identity to overcome loss of compactness caused by the Coulomb exponent ...
Jingai Du, Pengfei He, Hongmin Suo
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Boundary charges and integral identities for solitons in (d+1)-dimensional field theories
Nuclear Physics B, 2017 We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions.
Sven Bjarke Gudnason +2 more
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Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
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Identity and identity formation
, 2005 It seems that everywhere one looks at present, the notion of 'identity' is being discussed. From very dense intellectual publications to the popular press; from Pete Townsend asking, in the Who's classic 1978 track, 'Who Are You?' to Sandra Bullock's ...
Austin, Jon
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Boundary Value ProblemsThis paper is devoted to the existence of singular limit solutions for a nonlinear elliptic system of Liouville type under Navier boundary conditions in a bounded open domain of R 4 $\mathbb{R}^{4}$ .
Sami Baraket +3 more
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Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian
Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℝN, where N ≥ 3, F represents the primitive function of f, f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions
Sarah Abdullah Qadha +4 more
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Journal of Mathematics, Volume 2025, Issue 1, 2025.In this paper, our goal is to prove the existence of a weak solution (in H01Ω) for a fully nonlinear Dirichlet problem with a nonmonotone (e.g., Lipschitz) convection function F that depends on ∇u, and a nonlinearity G that is not necessarily monotone and depends on the solution function u, and the higher order term is −ΔΓ(x, u) − diva(x, u, ∇u ...
Teffera M. Asfaw +3 more
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Identity Formation in Adulthood : A Longitudinal Study from Age 27 to 50
, 2016 Longitudinal patterns of identity formation were analyzed in a representative cohort group of Finnish men and women born in 1959 across ages 27, 36, 42, and 50. The data were drawn from the Jyväskylä Longitudinal Study of Personality. Identity status (
Kokko, Katja +2 more
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The Calogero–Moser derivative nonlinear Schrödinger equation
Communications on Pure and Applied Mathematics, Volume 77, Issue 10, Page 4008-4062, October 2024.Abstract We study the Calogero–Moser derivative nonlinear Schrödinger NLS equation i∂tu+∂xxu+(D+|D|)(|u|2)u=0$$\begin{equation*} i\partial _t u +\partial _{xx} u + (D+|D|)(|u|^2) u =0 \end{equation*}$$posed on the Hardy–Sobolev space H+s(R)$H^s_+(\mathbb {R})$ with suitable s>0$s>0$.
Patrick Gérard, Enno Lenzmann
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