Related papers: Multiple solutions for a class of semilinear ellip…

We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…

We shall prove a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, \begin{equation}\label{con-c} \left \{ \begin{array}{ll} -\Delta u =|u|^{p-2} u+\mu |u|^{q-2}u, & x \in \Omega\\ u=0, & x…

We generalize our earlier results concerning meshfree collocation methods for semilinear elliptic second order problems to the quasilinear case. The stability question, however, is treated differently, namely by extending a paper on…

In this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special…

We establish the existence of multiple solutions for a nonvariational elliptic systems involving $p(x)$-Laplacian operator. The approach combines the methods of sub-supersolution and Leray--Schauder topological degree.

We introduce a probabilistic representation for solutions of quasilinear wave equation with analytic nonlinearities. We use stochastic cascades to prove existence and uniqueness of the solution.

We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as…

In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical approach is inspired by the Localized Orthogonal Decomposition…

We consider nonlinear elliptic equations which contains global coupling as a nonlinear term. We classify the existence of all possible positive solutions to this problem.

The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.

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 article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…

We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives,…

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…

For the system of semilinear elliptic equations \[ \Delta V_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in $\mathbb{R}^N$} \] we devise a new method to construct entire solutions. The method extends the existence results…

We obtain a pair of nontrivial solutions for a class of concave-linear-convex type elliptic problems that are either critical or subcritical. The solutions we find are neither local minimizers nor of mountain pass type in general. They are…

This paper is concerned with the structure of the solutions to subcritical elliptic equations related to the Matukuma equation. In certain cases the complete structure of the solution set is known, and is comparable to that of the original…

In this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the Hardy potential.

A Robin boundary-value problem with non-homogeneous differential operator, indefinite potential, and reaction defined only near zero is investigated. The existence of one or more nodal solutions is achieved by using truncation,…

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…