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Boundary Value ProblemsWe establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence ...
Weiwei Zhao +3 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we discus the existence of solutions for Riemann- Liouville fractional differential inclusions supplemented with Erdélyi- Kober fractional integral conditions.
Ahmad Bashir, Ntouyas Sotiris K.
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A proof of Liouville’s theorem [PDF]
Proceedings of the American Mathematical Society, 1961 1. S. Bochner, Group invariance of Cauchy's formula in several variables, Ann. of Math. vol. 45 (1944) pp. 686-707. 2. E. Heinz, Ein v. Neumannscher Satz iuber beschriinkte Operatoren im Hilbertschen Raum, Nachr. Akad. Wiss. Gottingen. Math.-Phys. Kl. Ila. (1952) pp. 5-6. 3. J.
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Liouville theorems for Dirac-harmonic maps [PDF]
Journal of Mathematical Physics, 2007 We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn, and a Riemannian manifold Sn (n⩾3) with the Schwarzschild metric to any Riemannian manifold N.
Chen, Qun, Jost, Jürgen, Wang, Guofang
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Gradient estimates for semilinear elliptic systems and other related results [PDF]
, 2014 A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville Theorem for general phase transition potentials.
Smyrnelis, Panayotis
core
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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Boundary value problems of fractional q-difference equations on the half-line
Boundary Value Problems, 2019 In this paper, we consider the boundary value problem of a class of nonlinear fractional q-difference equations involving the Riemann–Liouville fractional q-derivative on the half-line.
Kuikui Ma, Xinhui Li, Shurong Sun
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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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SOME REMARKS ON LIOUVILLE TYPE THEOREMS [PDF]
Recent Advances in Nonlinear Analysis, 2008 The goal of this note is to present elementary proofs of statements related to the Liouville theorem.
Brezis, H, Chipot, M, Xie, Y
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
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