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Singular limits of anisotropic Ginzburg-Landau functional
Springer Science and Business Media LLC - - 2020
Xing-Bin Pan
We derive the asymptotic behavior of the minimizers of the anisotropic Ginzburg-Landau functional of superconductivity, as the ratio between the largest and smallest effective masses is very big, hence the effective mass tensor becomes very degenerate.
One-iteration reconstruction algorithm for geometric inverse source problem
Springer Science and Business Media LLC - Tập 4 Số 1 - Trang 177-205 - 2018
Mourad Hrizi, Maatoug Hassine
Symmetric-Convex Functionals of Linear Growth
Springer Science and Business Media LLC - Tập 2 - Trang 59-71 - 2017
Franz Gmeineder
We discuss existence and regularity theorems for convex functionals of linear growth that depend on the symmetric rather than the full gradients. Due to the failure Korn’s Inequality in the L1-setup, the full weak gradients of minima do not need to exist, and the paper aims for presenting methods that help to overcome these issues as to partial regularity and higher integrability of minimisers.
Liouville theorems for superlinear parabolic problems with gradient structure
Springer Science and Business Media LLC - Tập 6 - Trang 145-153 - 2020
Pavol Quittner
We improve one of the methods for obtaining Liouville theorems for superlinear parabolic problems. In particular, if we consider a positively homogeneous gradient nonlinearity $$F:{{\mathbb {R}}}^m\rightarrow {{\mathbb {R}}}^m$$ of degree $$p>1$$, where $$n>2$$, $$p... hiện toàn bộ
Well-posedness, analyticity and time decay of the 3D fractional magneto-hydrodynamics equations in critical Fourier-Besov-Morrey spaces with variable exponent
Springer Science and Business Media LLC - Tập 8 - Trang 723-742 - 2022
Achraf Azanzal, Chakir Allalou, Said Melliani
In this paper, we establish the global well-posedness and analyticity of the 3D fractional magnetohydrodynamics equations in the critical Fourier-Besov-Morrey spaces with variable exponent, which can be seen as a meaningful complement to the corresponding results of the magnetohydrodynamics equations in usual Fourier-Besov-Morrey spaces. Furthermore, we get time decay rate estimate of mild solutio...... hiện toàn bộ
Positive Solutions for a Class of Nonlocal Problems Involving Lebesgue Generalized Spaces: Scalar and System Cases
Springer Science and Business Media LLC - Tập 2 - Trang 235-266 - 2017
Gelson C. G. Dos Santos, Giovany M. Figueiredo
In this work we prove the existence of positive solutions for a class of scalar nonlocal problems and systems of such equations. We use sub-supersolution method combined withfixed point arguments and apply the results to some concrete problems.
Global existence and blow-up of solutions for a $$\mathtt {p}$$ -Kirchhoff type parabolic equation with logarithmic nonlinearity
Springer Science and Business Media LLC - Tập 8 - Trang 919-938 - 2022
Mahammad Khuddush, Rajendra Prasad Kapula, Sa-Botta Bharathi
In this paper a class of $$\mathtt {p}$$ -Kirchhoff type parabolic equation with logarithmic nonlinearity is considered. By applying Galerkin’s approximation and the modified potential well method, some sufficient conditions are obtained for the existence of global and finite blow up of solutions.
Nonlinear scalar field equations with Berestycki–Lions’ nonlinearity on large domains
Springer Science and Business Media LLC - Tập 6 - Trang 711-731 - 2020
Yohei Sato, Masataka Shibata
We prove the existence of solutions for the following semilinear elliptic equation: $$\begin{aligned} - \Delta u = g(u) \quad \text {in } \Omega , \quad u \in H^1_0(\Omega ). \end{aligned}$$ Here $$\Omega $$ is a suitable large domain and g satisfies the completely same conditions as Berestycki–Lions’ conditions. Those conditions of g are known as “almost sufficient and necessary conditions” ...... hiện toàn bộ
A Moser–Trudinger type inequality on the Orlicz fractional space
Springer Science and Business Media LLC - Tập 9 - Trang 33-62 - 2022
Abderrahmane Lakhdari, Nedra Belhaj Rhouma, Mounir Hsini
We prove the existence of a weak solution to the perturbed fractional Kirchhoff problem with a singular exponential nonlinearity that includes the fractional $$\varphi$$ -laplacian operator. Our main results are obtained using Ekeland’s variational principle and the mountain pass theorem. To this e...... hiện toàn bộ
Existence and multiplicity of non-trivial solutions for fractional Schrödinger–Poisson systems with a combined nonlinearity
Springer Science and Business Media LLC - - Trang 1-14 - 2024
M. Soluki, G. A. Afrouzi, S. H. Rasouli
In this paper, we are concerned with the following fractional Schrödinger–Poisson system: $$\begin{aligned} \left\{ \begin{array}{ll} \displaystyle (-\Delta )^s u + V(x)u +\lambda \phi u=K(x){|u|}^ {q-2}u+ f(x,u), &{}\qquad \ x \in \mathbb {R}^3 \\ \displaystyle (-\Delta )^t\phi = u^2,&{} \qquad \ x \in \mathbb {R}^3\\ \end{array}\right...... hiện toàn bộ
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