Related papers: The moving plane method for doubly singular ellipt…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple…
In this paper we develop an $hp$-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and…
In this paper, we establish various maximum principles and develop the method of moving planes and the sliding method (on general unbounded domains) for equations involving the uniformly elliptic nonlocal Bellman operator. As a consequence,…
We study ground state solutions for linear and nonlinear elliptic PDEs in $\mathbb{R}^n$ with (pseudo-)differential operators of arbitrary order. We prove a general symmetry result in the nonlinear case as well as a uniqueness result for…
We investigate the qualitative properties of positive solutions to mixed local-nonlocal equations with indefinite nonlinearities, emphasizing the interaction between classical and fractional Laplacians. We first establish maximum principles…
We study the existence and multiplicity of solutions to the elliptic system where RN is a bounded and smooth domain. Using fibering maps and extracting Palais-Smale sequences in the Nehari manifold, we prove the existence of at least two…
This paper deals with existence of positive solutions for a class of quasilinear elliptic systems involving the $\Phi$-Laplacian operator and convex-concave singular terms. Our approach is based on the generalized Galerkin Method along with…
In the present work, we establish the existence of two positive solutions for singular nonlocal elliptic systems. More precisely, we consider the following nonlocal elliptic problem: $$\left\{\begin{array}{lll} (-\Delta)^su +V_1(x)u =…
We consider a semilinear elliptic equation on a smooth bounded domain $\Om$ in $\R^2$, assuming that both the domain and the equation are invariant under reflections about one of the coordinate axes, say the y-axis. It is known that…
We are concerned with the asymptotic analysis of positive blow-up boundary solutions for a class of quasilinear elliptic equations with absorption term. By means of the Karamata theory we establish the first two terms in the expansion of…
In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consider is a generalization of the Lichnerowicz equation that one…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
Solving elliptic PDEs in more than one dimension can be a computationally expensive task. For some applications characterised by a high degree of anisotropy in the coefficients of the elliptic operator, such that the term with the highest…
In this work, we develop an efficient solver based on neural networks for second-order elliptic equations with variable coefficients and singular sources. This class of problems covers general point sources, line sources and the combination…
Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a (generally branched) solution with leading order behaviour proportional to (z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic at z_0 and…
We use a simple method that leads to the integrals involved in obtaining the traveling wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in…
In this paper we discuss the relationship between the moving planes of a rational parametric surface and the singular points on it. Firstly, the intersection multiplicity of several planar curves is introduced. Then we derive an equivalent…
This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…
We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving…