Related papers: Three solutions to discrete anisotropic problems w…
We consider a Dirichlet problem driven by the anisotropic $(p,q)$-Laplacian and with a reaction that has the competing effects of a singular term and of a parametric superlinear perturbation. Based on variational tools along with truncation…
We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear)…
We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…
We present for the first time an explicit, complete and closed-form solution to the three-dimensional problem of two fixed centres, based on Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our…
We generalize the previous study on the application of variational autoencoders to the two-dimensional Ising model to a system with anisotropy. Due to the self-duality property of the system, the critical points can be located exactly for…
This article concerns on the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus. We prove that there exist three nontrivial solutions when the parameter is enough small via the variational methods and…
In this paper, we review several results from singularly perturbed differential equations with multiple small parameters. In addition, we develop a general conceptual framework to compare and contrast the different results by proposing a…
In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.
We prove new multiplicity results for some elliptic problems with critical exponential growth. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain…
We establish the existence and nonexistence of entire solutions to a semilinear elliptic problem whose nonlinearity is the critical power multiplied by a function that takes the value 1 in an open bounded region and the value -1 in its…
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer.…
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
By means of nonsmooth critical point theory, we prove existence of three weak solutions for an ordinary differential inclusion of Sturm-Liouville type involving a general set-valued reaction term depending on a parameter, and coupled with…
A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a…
A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a…
We consider an anisotropic version of Baxter's model of `sticky hard spheres', where a nonuniform adhesion is implemented by adding, to an isotropic surface attraction, an appropriate `dipolar sticky' correction (positive or negative,…
Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…
In this paper we consider a fully third order nonlinear boundary value problem which is of great interest of many researchers. First we establish the existence, uniqueness of solution. Next, we propose simple iterative methods on both…