On an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with variable singular and sublinear nonlinearities

Mustafa Avci; Mustafa Avci

doi:10.3934/cam.2024026

Communications in Analysis and Mechanics

2024, Volume 16, Issue 3: 554-577. doi: 10.3934/cam.2024026

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Research article

On an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with variable singular and sublinear nonlinearities

Mustafa Avci ^,

Faculty of Science and Technology, Applied Mathematics, Athabasca University, AB, Canada

Received: 20 February 2024 Revised: 29 July 2024 Accepted: 29 July 2024 Published: 06 August 2024
35A15, 35A21, 35J75, 58E30

In the present paper, we study an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with combined effects of variable singular and sublinear nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case where the variable singularity $ \beta(x) $ assumes its values in the interval $ (1, \infty) $.
Citation: Mustafa Avci. On an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with variable singular and sublinear nonlinearities[J]. Communications in Analysis and Mechanics, 2024, 16(3): 554-577. doi: 10.3934/cam.2024026

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Abstract

In the present paper, we study an anisotropic $ \overset{\rightarrow }{p}(\cdot) $-Laplace equation with combined effects of variable singular and sublinear nonlinearities. Using the Ekeland's variational principle and a constrained minimization, we show the existence of a positive solution for the case where the variable singularity $ \beta(x) $ assumes its values in the interval $ (1, \infty) $.

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