Strictly positive solutions for one-dimensional nonlinear elliptic problems

2014/05/14 by Uriel Kaufmann, Kaufmann, Uriel, Iván Medri +1
Computer Science · Mathematics · #34B15 #34B18 #35J25 #35J61 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1405.3687

openalex publication_date 2014/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study existence and nonexistence of strictly positive solutions for the elliptic problems of the form Lu=m( x) u^p in a bounded open interval, with zero boundary conditions, where L is a strongly uniformly elliptic differential operator, p∈( 0,1) , and m is a function that changes sign. We also characterize the set of values p for which the problem admits a solution, and in addition an existence result for other nonlinearities is presented.

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