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We investigate the problem of the existence of trajectories asymptotic to elliptic equilibria of Hamiltonian systems in the presence of resonances.
We investigate the problem of the existence of first integrals for multidimensional and ordinary linear differential systems with constant coefficients. The spectral method of the first integrals basis construction for these systems of…
The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of…
In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the…
The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…
We consider a nonlinear elliptic equation driven by the Dirichlet $p$-Laplacian with a singular term and a $(p-1)$-linear perturbation which is resonant at $+\infty$ with respect to the principal eigenvalue. Using variational tools,…
We are concerned with the existence and boundary behaviour of positive radial solutions for the system \begin{equation*} \left\{ \begin{aligned} \Delta u&=|x|^{a}v^{p} &&\quad\mbox{ in } \Omega, \\ \Delta v&=|x|^{b}v^{q}f(|\nabla u|)…
Given a bivariate system of polynomial equations with fixed support sets $A, B$ it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity $i$ for all $i$ in the…
We consider a forced oscillation and passage through resonance for an infinite-length system, having time-varying parameters and possessing a single trapped mode. The system is a string, lying on the Winkler foundation and equipped with a…
We consider radially symmetric solutions for a class of resonant problems on a unit ball $B \subset R^n$ around the origin \[ \Delta u+\la _1 u +g(u)=f(r) \s \mbox{for $x \in B$}, \s u=0 \s \mbox{on $\partial B$} \,. \] Here the function…
It is shown how to define difference equations on particular lattices $\{x_n\}$, $n\in\mathbb{Z}$, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…
Based on a variant of frequency function, we improve the vanishing order of solutions for Schr\"{o}dinger equations which describes quantitative behavior of strong uniqueness continuation property. For the first time, we investigate the…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when…
In the present work, we establish the existence and multiplicity of positive solutions for the singular elliptic equations with a double weighted nonlocal interaction term defined in the whole space $\mathbb{R}^N$. The nonlocal term and the…
The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…