On a Class of Mixed Local and Nonlocal Semilinear Elliptic Equation with Singular Nonlinearity

Prashanta Garain

doi:10.1007/s12220-023-01262-5

On a Class of Mixed Local and Nonlocal Semilinear Elliptic Equation with Singular Nonlinearity

Prashanta Garain

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

14 Scopus citations

Abstract

In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish the existence of at least one weak solution for a parameter-dependent singular nonlinearity and existence of multiple solutions for perturbed singular nonlinearity. Our argument is based on the variational and approximation approach.

Original language	English
Article number	212
Journal	Journal of Geometric Analysis
Volume	33
Issue number	7
DOIs	https://doi.org/10.1007/s12220-023-01262-5
State	Published - 1 Jul 2023
Externally published	Yes

Keywords

Existence
Mixed local and nonlocal equation
Regularity
Singular nonlinearity

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-023-01262-5

Cite this

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title = "On a Class of Mixed Local and Nonlocal Semilinear Elliptic Equation with Singular Nonlinearity",

abstract = "In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish the existence of at least one weak solution for a parameter-dependent singular nonlinearity and existence of multiple solutions for perturbed singular nonlinearity. Our argument is based on the variational and approximation approach.",

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author = "Prashanta Garain",

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AB - In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, we establish the existence of at least one weak solution for a parameter-dependent singular nonlinearity and existence of multiple solutions for perturbed singular nonlinearity. Our argument is based on the variational and approximation approach.

KW - Existence

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KW - Regularity

KW - Singular nonlinearity

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On a Class of Mixed Local and Nonlocal Semilinear Elliptic Equation with Singular Nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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