Related papers: Global asymptotic expansion for anisotropic singul…
We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the…
We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are…
In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is: $ \left\{ \begin{array}{ll} -\mathcal Q_{p}u =[H(Du)]^{q}+f(x)…
We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques…
In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which…
We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…
We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.
In this paper, we have discussed the gravitational collapse and expansion of charged anisotropic cylindrically symmetric gravitating source. To this end, the generating solutions of Einstein-Maxwell field equations for the given source and…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by…
In the study of concavity properties of positive solutions to nonlinear elliptic partial differential equations the diffusion and the nonlinearity are typically independent of the space variable. In this paper we obtain new results aiming…
In this paper, we investigate the existence of weak solutions for a class of degenerate elliptic Dirichlet problems with critical nonlinearity and a logarithmic perturbation
In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…
We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify…
We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\epsilon$. This is the continuation of a precedent work by the first author. We construct two families of sectorial meromorphic…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…
The Dirichlet problem in arbitrary domains for a wide class of anisotropic elliptic equations of the second order with variable exponent nonlinearities and the right-hand side as a measure is considered. The existence of an entropy solution…
We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functions are used to characterize supplementary generalized…