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Stimulation of Neural Stem Cell Proliferation by Inhibition of Phosphodiesterase 5
Santos, Ana I.; Carreira, Bruno P.; Nobre, Rui J.; Carvalho, Caetana M.; Araujo, Ines M.The involvement of nitric oxide (NO) and cyclic GMP (cGMP) in neurogenesis has been progressively unmasked over the last decade. Phosphodiesterase 5 (PDE5) specifically degrades cGMP and is highly abundant in the mammalian brain. Inhibition of cGMP hydrolysis by blocking PDE5 is a possible strategy to enhance the first step of neurogenesis, proliferation of neural stem cells (NSC). In this work, we have studied...
A note on a class of problems for a higher-order fully nonlinear equation under...
Santos, Ana I.; Grossinho, Maria R.; Minhós, Feliz M.The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation u⁽ⁿ⁾(t)=f(t,u(t),u′(t),…,u⁽ⁿ⁻¹⁾(t)), n≥2, with the boundary conditions u^{(i)}(a) = A, for i=0,⋯,n-3, u⁽ⁿ⁻¹⁾(a) = B, u⁽ⁿ⁻¹⁾(b)=C or u^{(i)}(a)=A, for i=0,⋯,n-3, c₁u⁽ⁿ⁻²⁾(a)-c₂u⁽ⁿ⁻¹⁾(a)=B, c₃u⁽ⁿ⁻²⁾(b)+c₄u⁽ⁿ⁻¹⁾(b)=C, with A_{i},B,C∈R, for i=0,⋯,n-3, and c₁, c₂, c₃, c₄ re...
Solvability for a third order discontinuous fully equation with nonlinear funct...
Santos, Ana I.; Cabada, Alberto; Minhós, Feliz M.We prove an existence and location result for the third order functional nonlinear boundary value problem u′′′(t) = f(t,u,u′(t),u′′(t)), for t∈[a,b], 0 = L₀(u,u′,u(t₀)), 0 = L₁(u,u′,u′(a),u′′(a)), 0 = L₂(u,u′,u′(b),u′′(b)), with t₀∈[a,b] given, f:I×C(I)×R²→R is a L¹- Carathéodory function allowing some discontinuities on t and L₀,L₁, L₂ are continuous functions depending functionally on u and u′. The a...
A fourth order BVP of Sturm-Liouville with asymmetric unbounded nonlinearities
Santos, Ana I.; Minhós, Feliz M.; Gyulov, ThiomirIt is obtained an existence and location result for the fourth order boundary value problem of Sturm-Liouville type u^(iv)(t)=f(t,u(t),u′(t),u′′(t),u′′′(t)), for t∈[0,1], u(0)=u(1)=A, k₁u′′′(0)-k₂u′′(0)=0, k₃u′′′(1)+k₄u′′(1)=0, where f:[0,1]×R⁴→R is a continuous function and A,k_i∈R, for i=1,...,4, are such that k₁,k₃>0, k₂,k₄≥0. We assume that f verifies a one-sided Nagumo type growth condition which allows an...
Existence and location result for a fourth order boundary value problems
Santos, Ana I.; Minhós, Feliz M.; Gyulov, ThiomirIn the present work we prove an existence and location result for the fourth order fully nonlinear equation u^(iv)=f(t,u,u′,u′′,u′′′), 0<t<1, with the Lidstone boundary conditions u(0)=u′′(0)=u(1)=u′′(1)=0, where f:[0,1]×R⁴→R is a continuous function satisfying a Nagumo type condition. The existence of at least a solution lying between a pair of well ordered lower and upper solutions is obtained using an...
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