Partial-limit Solutions and Rational Solutions with Parameter for the Fokas-Lenells Equation

A partial-limit procedure is applied to soliton solutions of the Fokas-Lenells equation. Multiple-pole solutions related to real repeated eigenvalues are obtained. For the envelop | u | 2 , the simplest solution corresponds to a real double eigenvalue, showing a solitary wave with algebraic decay. Two such solitons allow elastic scattering but asymptotically with zero phase shift. Single eigenvalue with higher multiplicity gives rise to rational solutions which contain an intrinsic parameter, live on a zero background, and have slowly-changing amplitudes.

Multiple Solutions for Elliptic px,qx-Kirchhoff-Type Potential Systems in Unbounded Domains

In this paper, we establish the existence of at least three weak solutions for a parametric double eigenvalue quasi-linear elliptic px,qx-Kirchhoff-type potential system. Our approach is based on a variational method, and a three critical point theorem is obtained by Bonano and Marano.

Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()-Laplacian Operator

Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()-Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent three-critical-point theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.