Existence Results for p1(x,·) and p2(x,·) Fractional Choquard–Kirchhoff Type Equations with Variable s(x,·)-Order

Abstract

In this article, we study a class of Choquard–Kirchhoff type equations driven by the variable s(x,·)-order fractional p1(x,·) and p2(x,·)-Laplacian. Assuming some reasonable conditions and with the help of variational methods, we reach a positive energy solution and a negative energy solution in an appropriate space of functions. The main difficulties and innovations are the Choquard nonlinearities and Kirchhoff functions with the presence of double Laplace operators involving two variable parameters.

Platelet Behavior Contributes to Neuropathologies: A Focus on Alzheimer's and Parkinson's Disease

“…2 3 4 In addition, these diseases carry a burden of infection. 5 6 7 8 9 Moreover, inflammatory reactions overlap with pathways of vascular dysfunction and coagulopathy. These insights have led to new frameworks for understanding the pathogenesis of neurodegenerative conditions, such as considering infections as providing a trigger for the immune system, and central and peripheral inflammation as facilitating and aggravating disease pathogenesis.…”

“…Both AD and PD carry a burden of infection. 5 6 Indeed, external pathogens like bacteria (and their products such as lipopolysaccharide [LPS] and gingipain) and viruses are associated with (and sometimes argued as causative of) AD and PD 7 8 41 ( Table 2 ). Bacteria can cross the BBB via transcellular traversal, paracellular traversal, and as Trojan horses utilizing infected immune cells and viruses can infect endothelial cells to cross the BBB.…”