Nonexistence of Positive Solutions for System of Hadamard Fractional BVPs with P-Laplacian Operator

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DOI: https://doi.org/10.28924/2291-8639-24-2026-133
Published: Apr 30, 2026
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Sabbavarapu Nageswara Rao, Nonexistence of Positive Solutions for System of Hadamard Fractional BVPs with P-Laplacian Operator, Int. J. Anal. Appl., 24 (2026), 133.

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Sabbavarapu Nageswara Rao

Abstract

In this paper, we investigate a system of nonlinear Hadamard fractional differential equations involving \((p_1,p_2,p_3)\)-Laplacian operators subject to three-point boundary conditions. By constructing appropriate Green's functions and establishing their qualitative properties, the given boundary value problem is transformed into an equivalent system of nonlinear integral equations in a cone of a Banach space. Using fixed point arguments and sharp integral inequalities, we derive sufficient conditions ensuring the nonexistence of positive solutions. In particular, explicit bounds on the involved parameters are obtained under which the associated operator fails to admit fixed points. The results cover both sublinear-type growth conditions and superlinear-type lower bounds on the nonlinearities. These findings extend existing nonexistence results for fractional boundary value problems to the setting of coupled systems with Hadamard fractional derivatives and \(p\)-Laplacian operators.

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