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
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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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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