Related papers: Local and global properties of p-Laplace Henon equ…
We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schr\"odinger systems with magnetic field involving local and nonlocal nonlinearities.
We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of…
This is the final version, to appear in Commentarii Mathematici Helvetici.
In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.
We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity…
We present infinitely many solutions of the general Heun equation in terms of generalized hypergeometric functions. Each solution assumes that two restrictions are imposed on the involved parameters: a characteristic exponent of one of the…
We begin the paper with a Hopf's lemma for a fractional p-Laplacian problem on a half-space. Specifically speaking, we show that the derivative of the solution along the outward normal vector is strictly positive on the boundary of the…
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…
A nonlinearly generalized Camassa-Holm equation, depending an arbitrary nonlinearity power $p \neq 0$, is considered. This equation reduces to the Camassa-Holm equation when $p=1$ and shares one of the Hamiltonian structures of the…
Local and global properties of minimal solutions for the heat equation generated by the Dirichlet fractional Laplacian negatively perturbed by Hardy's potentials on open subsets of $\R^d$ are analyzed. As a byproduct we obtain instantaneous…
Locally bounded, local weak solutions to a special class of quasilinear, anisotropic, $p$-Laplacian type elliptic equations, are shown to be locally H\"older continuous. Homogeneous local upper bounds are established for local weak…
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions…
We study the boundary behavior of solutions to fractional elliptic equations. As the first result, the isolation of the first eigenvalue of the fractional Lane-Emden equation is proved in the bounded open sets with Wiener regular boundary.…
In this paper we study a H\'enon-like equation (see equations (1) below), where the nonlinearity f(t) is not homogeneous (i.e., it is not a power). By minimization on the Nehari manifold, we prove that for large values of the parameter…
In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish existence of at least one weak solution for a parameter dependent singular nonlinearity…
In this work we study the existence and regularity of solutions to the following equation: $$-\Delta_p u + g(x) u = \frac{\lambda}{|x|^{p}} |u|^{p-2}u + f,$$ where $1< p < N$ and $f\in L^m$, where $m\ge 1$.
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
We study a second order ordinary differential equation corresponding to rotationally symmetric $p$-harmonic maps. We show unique continuation and Liouville's type theorems for positive solutions. We discuss the existence of bounded positive…
This paper is devoted to the study of semi-stable radial solutions $u\in H^1(B_1)$ of $-\Delta u=\vert x\vert^\alpha f(u) \mbox{ in } B_1\setminus\lbrace0\rbrace$, where $f\in C^1(\mathbb{R})$ is a general nonlinearity, $\alpha>-2$ and…