Existence, nonexistence, and multiplicity of solutions for the fractional p & q $p\&q$ -Laplacian equation in R N $\mathbb{R}^{N}$

Abstract

In this paper, we study the existence, nonexistence, and multiplicity of solutions to the following fractional p&q-Laplacian equation:where λ is a real parameter, (-)

Aligned core/shell electrospinning of poly(glycerol sebacate)/poly(l‐lactic acid) with tuneable structural and mechanical properties

“…The maximum strain applied was 15%, which is typical of the dynamic loading strain of soft tissues, such as cardiac muscle, under normal physiological conditions. 2,33 The resilience of a material was calculated as the mean from the stress-strains curves of ten cyclic deformations using the following equation: 34 Resilience (%) = Area under unloading curve Area under loading curve (2) Biological tissues are usually found to exhibit nonlinear elasticity and several constitutive equations have been proposed for this behaviour. 1,35 -37 These functions predict that stress increases near-exponentially with strain.…”

“…In contrast to the behaviour of the PLLA fibre mats which show permanent deformation after small levels of strain due to their thermoplastic nature, the stress-strain behaviour of the PGS/PLLA fibre mats is convex to the strain axis (or 'J-shaped') and this behaviour is typical of natural soft tissues. 2 This behaviour is believed to be associated with the elastomeric nature of the core of the fibres and the physical nature of the fibrous mat. Table 3 and Fig.…”

“…20 Electrospun fibres can also enhance cellular alignment and guide the growth of cells, 20,21 and so the fabrication and mechanical properties of aligned fibre scaffolds have drawn more and more attention recently. 18 -26 In previous studies, it has been shown that fibre alignment can increase the modulus and strength of fibre scaffolds, 21,22,27 but the effects of the extent of fibre alignment on the nonlinear elasticity of these fibre mats, and especially the effects of fibre alignment on resilience and the stiffness constant (which characterizes the nonlinear J-shaped stress-strain curve 1,2 ), remain an open question.…”

“…Soft tissues exhibit nonlinear elastic stress-strain behaviour which is significantly different from that of the biodegradable thermoplastic polymers and their copolymers currently used for tissue repair. 1,2 The stress-strain curves of synthetic elastomers are comparatively linear (the stress rises proportionately with the strain until elongations of over 100% are reached) while biological tissues exhibit nonlinear J-shaped curves (the stress rises at an increasing rate as the strain is raised) at up to 15% strain. 3 The reason for this difference is that synthetic polymers are usually isotropic with randomly entangled molecular chains, whereas biological tissues are composed of proteins which contain aligned nanofibres.…”

“…Aligned fibre mats 2,18,19 can be produced by electrospinning of synthetic polymers, and it has been shown that aligned polymeric fibre scaffolds can mimic natural extracellular matrix better than non-aligned polymers. 20 Electrospun fibres can also enhance cellular alignment and guide the growth of cells, 20,21 and so the fabrication and mechanical properties of aligned fibre scaffolds have drawn more and more attention recently.…”