Solvability of linear and semilinear eigenvalue problems with \(L^ 1\) data
type: Item
instance of: scholarly article
title: Solvability of linear and semilinear eigenvalue problems with \(L^ 1\) data
zbMATH Open document ID: 0822.35106
author: Luigi Orsina
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1994-03-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108304
review text: Summary: We study the equation \[ A(u)= \lambda u+f \quad \text{in } \Omega, \qquad u=0 \quad \text{on } \partial \Omega, \] where \(A\) is a linear elliptic operator in divergence form, \(\lambda\) is a real number and \(f\) is a function belonging to \(L^ 1 (\Omega)\). We find existence results similar to those obtained in the case \(f\in L^ 2 (\Omega)\). Furthermore, we study the Landesmann-Lazer, Dolph and Ambrosetti-Prodi problems for the operator \(A\), always with \(L^ 1 (\Omega)\) data.
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 510106
zbMATH Keywords: linear elliptic operator
zbMATH Keywords: existence
zbMATH Keywords: Ambrosetti-Prodi problems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 510106