Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity
Advanced Nonlinear Studies, 2022 In the present paper, we study the existence of the normalized solutions for the following coupled elliptic system with quadratic nonlinearity −Δu−λ1u=μ1∣u∣u+βuvinRN,−Δv−λ2v=μ2∣v∣v+β2u2inRN,\left\{\begin{array}{ll}-\Delta u-{\lambda }_{1}u={\mu }_{1}| u|
Wang Jun, Wang Xuan, Wei Song
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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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On the problem of maximal $L^q$-regularity for viscous Hamilton-Jacobi equations
, 2020 For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q > d \frac{\gamma-1}\gamma$.Comment: 11 ...
Cirant, Marco, Goffi, Alessandro
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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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A multiplicity result for the scalar field equation
, 2013 We prove the existence of $N - 1$ distinct pairs of nontrivial solutions of the scalar field equation in ${\mathbb R}^N$ under a slow decay condition on the potential near infinity, without any symmetry assumptions.
Perera, Kanishka
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Finite reduction and Morse index estimates for mechanical systems [PDF]
, 2011 A simple version of exact finite dimensional reduction for the variational setting of mechanical systems is presented. It is worked out by means of a thorough global version of the implicit function theorem for monotone operators.
A. Bahri +18 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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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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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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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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