Existence and multiplicity results for semilinear equations with measure data

ALBERTO FERRERO; C. SACCON

Existence and multiplicity results for semilinear equations with measure data

ALBERTO FERRERO
, C. SACCON

Department of Science and Technological Innovation

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation -\Delta u = g(x, u) + \mu where \mu is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments front critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.

Original language	English
Pages (from-to)	285-318
Number of pages	34
Journal	Topological Methods in Nonlinear Analysis
Volume	28
Issue number	2
Publication status	Published - 1 Jan 2006

Keywords

Dirichlet problem
Radon measures
critical point theory.

Cite this

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title = "Existence and multiplicity results for semilinear equations with measure data",

abstract = "In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation -\textbackslash{}Delta u = g(x, u) + \textbackslash{}mu where \textbackslash{}mu is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments front critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.",

keywords = "Dirichlet problem, Radon measures, critical point theory., Dirichlet problem, Radon measures, critical point theory.",

author = "ALBERTO FERRERO and C. SACCON",

year = "2006",

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language = "English",

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pages = "285--318",

journal = "Topological Methods in Nonlinear Analysis",

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T1 - Existence and multiplicity results for semilinear equations with measure data

AU - FERRERO, ALBERTO

AU - SACCON, C.

PY - 2006/1/1

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N2 - In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation -\Delta u = g(x, u) + \mu where \mu is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments front critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.

AB - In this paper, we study existence and nonexistence of solutions for the Dirichlet problem associated with the equation -\Delta u = g(x, u) + \mu where \mu is a Radon measure. Existence and nonexistence of solutions strictly depend on the nonlinearity g(x, u) and suitable growth restrictions are assumed on it. Our proofs are obtained by standard arguments front critical theory and in order to find solutions of the equation, suitable functionals are introduced by mean of approximation arguments and iterative schemes.

KW - Dirichlet problem

KW - Radon measures

KW - critical point theory.

KW - Dirichlet problem

KW - Radon measures

KW - critical point theory.

UR - https://iris.uniupo.it/handle/11579/18435

M3 - Article

SN - 1230-3429

VL - 28

SP - 285

EP - 318

JO - Topological Methods in Nonlinear Analysis

JF - Topological Methods in Nonlinear Analysis

IS - 2

ER -

Existence and multiplicity results for semilinear equations with measure data

Abstract

Keywords

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