Journal•ISSN: 1230-3429
Topological Methods in Nonlinear Analysis
Juliusz Schauder University Center for Nonlinear Studies
About: Topological Methods in Nonlinear Analysis is an academic journal published by Juliusz Schauder University Center for Nonlinear Studies. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 1230-3429. Over the lifetime, 1455 publications have been published receiving 16082 citations.
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TL;DR: In this article, the eigenvalue problem for the Schrödinger operator coupled with the electromagnetic field E,H was studied and the case in which A and φ do not depend on the time t and ψ(x, t) = u(x)e, u real function and ω a real number was investigated.
Abstract: In this paper we study the eigenvalue problem for the Schrödinger operator coupled with the electromagnetic field E,H. The case in which the electromagnetic field is given has been mainly considered ([1]–[3]). Here we do not assume that the electromagnetic field is assigned, then we have to study a system of equations whose unknowns are the wave function ψ = ψ(x, t) and the gauge potentials A = A(x, t), φ = φ(x, t) related to E,H. We want to investigate the case in which A and φ do not depend on the time t and ψ(x, t) = u(x)e, u real function and ω a real number In this situation we can assume A = 0 and we are reduced to study the existence of real numbers ω and real functions u, φ satisfying the system
563 citations
Journal Article•
TL;DR: The homotopy perturbation method as discussed by the authors decomposes a complex problem under study into a series of simple problems that are easy to be solved, and thus is accessible to non-mathematicians and engineers.
Abstract: The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into a series of simple problems that are easy to be solved. This note gives an elementary introduction to the basic solution procedure of the homotopy perturbation method. Particular attention is paid to constructing a suitable homotopy equation.
285 citations
248 citations
221 citations
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TL;DR: In this article, the Dirichlet problem is considered for continuous functions and the Borel measure Fk[u] is defined for continuous continuous functions, where u ∈ C(Ω) is called k-convex if Fj [u] ≥ 0 (> 0) for j = 1,..., k.
Abstract: Alternatively we may write (1.3) Fk[u] = [Du]k, where [A]k denotes the sum of the k× k principal minors of an n× n matrix A. Our purpose in this paper is to extend the definition of the Fk to corresponding classes of continuous functions so that Fk[u] is a Borel measure and to consider the Dirichlet problem in this setting. A function u ∈ C(Ω) is called k-convex (uniformly k-convex) in Ω if Fj [u] ≥ 0 (> 0) for j = 1, . . . , k. The operator Fk
165 citations