Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval
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DOI: 10.1002/mma.4106
Abstract: In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D0+αu(t)+ft,u(t),D0+α−1u(t)=0,t∈(0,+∞), with the integral boundary conditions u(0)=0,D0+α−1u(∞)=∫0τg1(s)u(s)ds+a,D0+α−2u(0)=∫0τg2(s)u(s)ds+b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions… read more here.
Keywords: infinite interval; positive solutions; integral boundary; fractional differential ... See more keywords
Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Infinite Delay
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DOI: 10.1007/s40306-018-0289-5
Abstract: We consider a class of semilinear parabolic equations with infinite delay and nonlinearity of polynomial type. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we show the… read more here.
Keywords: semilinear parabolic; asymptotic behavior; infinite delay; parabolic equations ... See more keywords
Solutions of third order degenerate equations with infinite delay in Banach spaces
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DOI: 10.1007/s43037-020-00058-x
Abstract: We study the well-posedness of the third order degenerate differential equations with infinite delay$$(P_3): (Mu)'''(t) + (Lu)''(t) + (Bu)'(t)= Au(t) + \int _{-\infty }^t a(t-s)Au(s)ds + f(t){\text{ on }}[0, 2\pi ]$$in Lebesgue–Bochner spaces $$L^p(\mathbb{T};\; X)$$… read more here.
Keywords: equations infinite; order degenerate; infinite delay; third order ... See more keywords
Yamabe equations on infinite graphs
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DOI: 10.1016/j.jmaa.2017.12.020
Abstract: Abstract We concern in this paper the graph Yamabe equation Δ u + h u = g | u | p − 2 u , with known functions h and g on an infinite graph,… read more here.
Keywords: infinite graphs; yamabe equations; graph; equations infinite ... See more keywords
Inertial manifolds for functional differential equations with infinite delay
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DOI: 10.1142/s1793557122500450
Abstract: In this paper, we consider a class of functional differential equations with infinite delay in a real separable Hilbert space. By using the Lyapunov–Perron method, we prove the existence of inertial manifolds for mild solutions.… read more here.
Keywords: functional differential; equations infinite; infinite delay; differential equations ... See more keywords
Solving a System of Differential Equations with Infinite Delay by Using Tripled Fixed Point Techniques on Graphs
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DOI: 10.3390/sym14071388
Abstract: In this manuscript, some similar tripled fixed point results under certain restrictions on a b−metric space endowed with graphs are established. Furthermore, an example is provided to support our results. The obtained results extend, generalize,… read more here.
Keywords: fixed point; infinite delay; differential equations; tripled fixed ... See more keywords