Results 31 to 40 of about 11,870,254 (353)
Ground states for a fractional scalar field problem with critical growth [PDF]
Differential and Integral Equations, 2016 We prove the existence of a ground state solution for the following fractional scalar field equation $(-\Delta)^{s} u= g(u)$ in $\mathbb{R}^{N}$ where $s\in (0,1), N> 2s$,$ (-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R ...
V. Ambrosio
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Electronic Journal of Differential Equations, 2021 In this article, we study a class of critical fractional Schrodinger-Poisson system with two perturbation terms. By using variational methods and Lusternik-Schnirelman category theory, the existence of ground state and two nontrivial solutions are ...
Lintao Liu, Kaimin Teng
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Positive solutions of a Kirchhoff–Schrödinger--Newton system with critical nonlocal term
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper deals with the following Kirchhoff–Schrödinger–Newton system with critical growth \begin{equation*} \begin{cases} \displaystyle-M\left(\int_{\Omega}|\nabla u|^2dx\right)\Delta u=\phi |u|^{2^*-3}u+\lambda|u|^{p-2}u, &\rm \mathrm{in ...
Ying Zhou +3 more
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Ground state solutions for a fractional Schrödinger equation with critical growth [PDF]
Asymptotic Analysis, 2016 In this paper we investigate the existence of nontrivial ground state solutions for the following fractional scalar field equation ( − Δ ) s u + V ( x ) u = f ( u ) in R N , where s ∈ ( 0 , 1 ) , N > 2 s , ( − Δ ) s is the fractional Laplacian, V : R N →
V. Ambrosio, G. Figueiredo
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Slip Line Growth as a Critical Phenomenon
Physical Review Letters, 2009 We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up undergoes a second order non-equilibrium phase transition as a function of stress, which can be characterized by ...
Fabio Leoni, Stefano Zapperi
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Complexity and Criticality in Laplacian Growth Models [PDF]
Europhysics Letters (EPL), 1993 7pages.
Enrique Louis, O. Pla, Francisco Guinea
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Topological Methods in Nonlinear Analysis, 2019 We establish a version of the Trudinger-Moser inequality involving unbounded or decaying radial weights in weighted Sobolev spaces. In the light of this inequality and using a minimax procedure we also study existence of solutions for a class of ...
F. Albuquerque, S. Aouaoui
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Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation
Nonlinear Analysis, 2021 In this paper, we get the existence of two positive solutions for a fourth-order problem with Navier boundary condition. Our nonlinearity has a critical growth, and the method is a local minimum theorem obtained by Bonanno.
Lin Li, Donal O’Regan
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Elliptic equations with nearly critical growth
Journal of Differential Equations, 1987 The author studies what happens to the solution of the boundary value problem \[ (1)\quad -\Delta u=u^ p\quad u>0\quad in\quad \Omega \in R^ N;\quad u=0\quad on\quad \partial \Omega \] if p approaches the critical Sobolev exponent \(p=(N+2)/(N-2)\) (if \(p\geq (N+2)/(N-2)\), the problem (1) has no solutions) and \(\Omega =B_ R=\{x\in R^ N ...
F. V. Atkinson, Lambertus A. Peletier
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Singularly Perturbed Fractional Schrödinger Equations with Critical Growth
Advanced Nonlinear Studies, 2018 We are concerned with the following singularly perturbed fractional Schrödinger equation:
He Yi
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