Related papers: Singular phenomena in nonlinear elliptic problems.…
We study an elliptic problem with exponential nonlinearities describing the statistical mechanics equilibrium of point vortices with variable intensities. For suitable values of the physical parameters we exclude the existence of blow-up…
The theory of elliptic equations involving singular nonlinearities is well studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we…
In light of the question of finite-time blow-up vs. global well-posedness of solutions to problems involving nonlinear partial differential equations, we provide several cautionary examples which indicate that modifications to the boundary…
We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian. An extension procedure leads us to study a degenerate or…
We study a semilinear elliptic problem with a singular nonlinear term of the type $g(u)=-u^{-1}$, using a variational approach. Note that the minus sign is important since the corresponding term in the Euler-Lagrange functional is concave.…
In this paper, we investigate semilinear elliptic equations with general exponential-type nonlinearities in two dimensions. For such nonlinearities, we establish two main results. The first is the construction of a singular solution.…
We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type…
In this paper we consider the existence of positive solutions for a singular elliptic problem involving an asymtotically linear nonlinearity and depending on one positive parameter. Using variational methods, together with comparison…
In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new…
The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of…
We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a…
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial…
We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model…
We study the blow-up problem of one-dimensional nonlinear heat equations. Our result shows that for a certain class of initial conditions, the solutions blow up in finite time and we characterize the asymptotic dynamics of these solutions.…
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities are proved. Blow-up conditions are investigated too.
Boundedness and blow-up of solutions for a nonlinear elliptic system arising in probability and stochastic processes
In the present work we shall consider the existence and multiplicity of solutions for nonlocal elliptic singular problems where the nonlinearity is driven by two convolutions terms. More specifically, we shall consider the following…