Partial Differential Equations and Applications
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The effect of the domain topology on the number of positive solutions for an elliptic system
Partial Differential Equations and Applications - Tập 3 - Trang 1-23 - 2022
In this paper we prove an existence result of multiple positive solutions for the following system
$$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u= \frac{2 \alpha _\epsilon }{\alpha _\epsilon +\beta _\epsilon }|u|^{\alpha _\epsilon -2}u |v|^{\beta _\epsilon }&{} \text{ in } \Omega , \\ -\Delta v= \frac{2 \beta _\epsilon }{...... hiện toàn bộ
Multiple solutions for a class of fractional logarithmic Schrödinger equations
Partial Differential Equations and Applications - - 2021
Existence and nonexistence of solutions to nonlocal elliptic problems
Partial Differential Equations and Applications - Tập 3 - Trang 1-32 - 2022
It is established existence and nonexistence of solutions to nonlocal elliptic problems involving the generalized pseudo-relativistic Hartree equation. Our arguments are based on variational methods together with a fine analysis on the Pohozaev identity.
Regularity properties of the cubic biharmonic Schrödinger equation on the half line
Partial Differential Equations and Applications - Tập 2 - Trang 1-37 - 2021
In this paper we study the regularity properties of the cubic biharmonic Schrödinger equation posed on the right half line. We prove local well-posedness and obtain a smoothing result in the low-regularity spaces on the half line. In particular we prove that the nonlinear part of the solution on the half line is smoother than the initial data obtaining a full derivative gain in certain cases. More...... hiện toàn bộ
Sobolev spaces and functions of Marcinkiewicz type with repeated averaging operations over spheres
Partial Differential Equations and Applications - - 2022
On the mathematical analysis of the artificial compressibility method
Partial Differential Equations and Applications - Tập 2 Số 5 - Trang 1-19 - 2021
Recent results on the stability of bifurcating solutions of the artificial compressible system with small artificial Mach numbers are reviewed. A perturbation result on the spectrum of linearized operators around stationary flows is also given when the artificial Mach number is sufficiently small.
Hardy type inequalities with spherical derivatives
Partial Differential Equations and Applications - Tập 1 Số 1 - 2020
Entire solutions with moving singularities for a semilinear heat equation with a critical exponent
Partial Differential Equations and Applications - Tập 3 - Trang 1-16 - 2022
We consider the semilinear heat equation
$$\partial _t u -\Delta u=u^{N/(N-2)}$$
in
$$\Omega $$
with
$$u=0$$
...... hiện toàn bộ
Nonlinear fractional Schrödinger equation on the half-Line
Partial Differential Equations and Applications - Tập 3 - Trang 1-27 - 2022
This paper study the local-in-time existence of solution for the nonlinear fractional Schrödinger equation with Levy indices
$$1<\alpha <2$$
on the half-line
$$i\partial _t u+(-\Delta ^+)^{\alpha /2}u+\lambda u|u|^{p-1}=0$$
...... hiện toàn bộ
Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on $${{\mathbb {R}}}^3$$ subject to attractive background charges
Partial Differential Equations and Applications - Tập 4 - Trang 1-10 - 2023
We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapp...... hiện toàn bộ
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