Related papers: Conformally invariant fully nonlinear elliptic equ…
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…
We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.
We provide a suitable variational approach for a class of nonlocal problems involving the fractional laplacian and singular nonlinearities for which the standard techniques fail. As a corollary we deduce a characterization of the solutions.
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…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Two essential methods, the symmetry analysis and of the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations are discussed. The main similarities and differences of these two different…
We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.
In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.
Mather and Yau showed that an isolated complex hypersurface singularity is completely determined by its moduli algebra. It is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and,…
We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
We construct positive weak solutions of a class of semilinear elliptic equation which vanish in suitable trace sense on the boundary of a given smooth bounded N-dimensional domain, but which are singular at prescribed isolated points of the…
In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -\Delta u+\frac{\mu}{|x|^2} u=u^p\quad {\rm in}\quad \Omega\setminus\{0\},\qquad…
In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.
We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…
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…
n this paper, we prove existence of nodal solutions for singular semilinear elliptic systems without variational structure where its both components are of sign changing. Our approach is based on sub-supersolutions method combined with…
In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in $\mathbb{C}^{n}$ without any curvature assumptions on the domain.
We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive…