Abstract The nonlinear eigenvalue problem of a class second order semi-transcendental differential equations is studied. A defined as the initial condition which gives rise separatrix solution. equation can be integrated once to first equation, e.g., Ricatti equation. It shown that problems these are equivalent linear problems. They share exactly same eigenvalues. eigensolutions in two closely ...

We investigate a technique to transform linear two-parameter eigenvalue problem into nonlinear (NEP). The transformation stems from an elimination of one the equations in problem, by considering it as (standard) generalized problem. characterize equivalence between original and nonlinearized theoretically show how use computationally. Special cases can be interpreted reversed companion lineariz...

In this paper, we study the quadratic tensor eigenvalue complementarity problem (QTEiCP). By a randomization process, complementarity(QC) eigenvalues are classified into two cases. For each case, QTEiCP is formulated as an equivalent generalized moment problem. The QC eigenvectors can be computed in order. Each of them solved by sequence semidefinite relaxations. We prove that such converges fi...

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of smoothness for P.D.E. We shall review some old results and present recent improvements on this sub...