Solutions behavior of mechanical oscillator equations with impulsive effects under Power Caputo fractional operator and its symmetric cases. [PDF]
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Liouville Type Theorems for Fractional Parabolic Problems
Journal of Dynamics and Differential Equations, 2021The authors establish Liouville-type theorems for fractional parabolic problems, presenting a compelling dual-purpose exploration. Their first objective is to establish optimal Liouville-type theorems, focusing on both nonnegative and positive supersolutions of fractional parabolic equations across the entire time-space continuum.
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A Theorem of Liouville Type for Harmonic Morphisms
Geometriae Dedicata, 2001Let \(M\) be a complete noncompact Riemannian manifold with nonnegative Ricci curvature and \(N\) be a Riemannian manifold with nonpositive scalar curvature. Then every harmonic morphism \(M\to N\) of finite energy is constant. This theorem is related to the classical result of \textit{R. Schoen} and \textit{S.-T. Yau} [Comment. Math. Helv. 51, 333-341
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A Liouville-type theorem for Lane-Emden system
Indiana University Mathematics Journal, 2002The authors provide a partial positive answer to a well-known conjecture about the nonexistence of positive solutions to Lane-Emden systems below the critical Sobolev hyperbola. The proof is based on a monotonicity argument for suitable transformed functions.
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