On multiplicity and concentration behavior of solutions for a critical system with equations in divergence form

2021 ◽  
Vol 494 (1) ◽  
pp. 124446
Author(s):  
Giovany M. Figueiredo ◽  
Segundo Manuel A. Salirrosas
Author(s):  
Leanne SOBEL ◽  
Katrina SKELLERN ◽  
Kat PEREIRA

Design thinking and human-centred design is often discussed and utilised by teams and organisations seeking to develop more optimal, effective or innovative solutions for better customer outcomes. In the healthcare sector the opportunity presented by the practice of human-centred design and design thinking in the pursuit of better patient outcomes is a natural alignment. However, healthcare challenges often involve complex problem sets, many stakeholders, large systems and actors that resist change. High-levels of investment and risk aversion results in the status quo of traditional technology-led processes and analytical decision-making dominating product and strategy development. In this case study we present the opportunities, challenges and benefits that including a design-led approach in developing complex healthcare technology can bring. Drawing on interviews with participants and reflections from the project team, we explore and articulate the key learning from using a design-led approach. In particular we discuss how design-led practices that place patients at the heart of technology development facilitated the project team in aligning key stakeholders, unearthing critical system considerations, and identifying product and sector-wide opportunities.


Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.


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