Results 31 to 40 of about 526 (85)
Existence of groundstates for a class of nonlinear Choquard equations [PDF]
, 2012 We prove the existence of a nontrivial solution (u \in H^1 (\R^N)) to the nonlinear Choquard equation [- \Delta u + u = \bigl(I_\alpha \ast F (u)\bigr) F' (u) \quad \text{in (\R^N),}] where (I_\alpha) is a Riesz potential, under almost necessary ...
Jean, Van Schaftingen, Vitaly Moroz
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Nonexistence of small, odd breathers for a class of nonlinear wave equations
, 2016 In this note, we show that for a large class of nonlinear wave equations with odd nonlinearities, any globally defined odd solution which is small in the energy space decays to $0$ in the local energy norm.
Kowalczyk, Michał +2 more
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Existence and concentration behavior of positive solutions to Schrödinger-Poisson-Slater equations
Advances in Nonlinear Analysis, 2023 This article is directed to the study of the following Schrödinger-Poisson-Slater type equation: −ε2Δu+V(x)u+ε−α(Iα∗∣u∣2)u=λ∣u∣p−1uinRN,-{\varepsilon }^{2}\Delta u+V\left(x)u+{\varepsilon }^{-\alpha }\left({I}_{\alpha }\ast | u{| }^{2})u=\lambda | u{| }^{
Li Yiqing, Zhang Binlin, Han Xiumei
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Advanced Nonlinear StudiesIn this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia +2 more
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New existence results for the mean field equation on compact surfaces via degree theory [PDF]
, 2014 We consider a class of equations with exponential non-linearities on a compact surface which arises as the mean field equation of the equilibrium turbulence with arbitrarily signed vortices. We prove an existence result via degree theory. This yields new
Jevnikar, Aleks
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Symmetries, Hopf fibrations and supercritical elliptic problems
, 2015 We consider the semilinear elliptic boundary value problem \[ -\Delta u=\left\vert u\right\vert ^{p-2}u\text{ in }\Omega,\text{\quad }u=0\text{ on }\partial\Omega, \] in a bounded smooth domain $\Omega$ of $\mathbb{R}^{N}$ for supercritical exponents $p>\
Clapp, Mónica, Pistoia, Angela
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Advances in Nonlinear Analysis, 2023 In this article, we study the existence of ground state solutions for the Schrödinger-Poisson-Slater type equation with the Coulomb-Sobolev critical growth: −Δu+14π∣x∣∗∣u∣2u=∣u∣u+μ∣u∣p−2u,inR3,-\Delta u+\left(\frac{1}{4\pi | x| }\ast | u{| }^{2}\right)u=|
Lei Chunyu, Lei Jun, Suo Hongmin
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A semilinear problem with a W^{1,1}_0 solution
, 2012 We study a degenerate elliptic equation, proving the existence of a W^{1,1}_0 distributional ...
Boccardo, Lucio +2 more
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Existence and Asymptotic Profile of Nodal Solutions to Supercritical Problems
Advanced Nonlinear Studies, 2017 We establish the existence of nodal solutions to the supercritical ...
Clapp Mónica, Pacella Filomena
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Reaction-diffusion problems on time-dependent Riemannian manifolds: stability of periodic solutions
, 2017 We investigate the stability of time-periodic solutions of semilinear parabolic problems with Neumann boundary conditions. Such problems are posed on compact submanifolds evolving periodically in time.
Bandle, Catherine +2 more
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