Instability of nonnegative solutions for a class of semilinear elliptic boundary value problems

AbstractWe consider the boundary value problem −Δu(x) = λf(u(x)), x ∈ Ω, Bu(x) = 0, x ∈ ∂Ω, where Ω is a bounded region in Rn with smooth boundary Bu(x) = αh(x)u + (1 − α)∂u∂n where α ∈ [0,1], h: ∂Ω → R+ with h = 1 when α = 1, λ > 0, f is a smooth function such that ƒ″(u) > 0 for u > 0, ƒ(u) < 0 for u ∈ (0,β) and ƒ(u) > 0 for u > β for some β > 0. We provide a simple proof to establish that every non-trivial nonnegative solution is unstable

Multiple Positive Solutions for a Class of Semipositone Neumann Two Point Boundary Value Problems

AbstractWe consider the two point Neumann boundary value problem −u″ = (x) = λƒ(u(x)); x ∈ (0, 1)u′(0) = 0 = u′(l) where λ is a positive parameter, ƒ ∈ C2[0, ∞), ƒ′(u) > 0 for u > 0, and for some β > 0, ƒ(u) < 0 for u ∈ [0, β) (semipositone) and ƒ′(u) > 0 for u > β. We discuss existence and multiplicity results for positive solutions. In particular, we prove that if the set S = (π2n2/ƒ′(β), θ2/−2F(β)), where n ∈ N, F(u) = ∫u0ƒ(s) ds and θ is the unique positive zero of F, is nonempty, then there exist at least 2n + 1 positive solutions for each λ ∈ S. Furthermore, if ƒ″ > 0 on [0, β) and ƒ″ < 0 on (β, ∞), then we prove that there are exactly 2n + 1 positive solutions for each λ ∈ S. We also discuss examples to which our results apply

An existence result for a semipositone problem with a sign changing weight

We establish an existence result on positive solution for a class of reaction-diffusion equation with semipositone structure. In particular, our results apply to the diffusive logistic equation with a class of sign changing weight and constant yield harvesting. We establish the result via the method of subsuper solutions

Positive Solutions of Quasilinear Boundary Value Problems

AbstractThis paper deals with the existence of positive solutions for the boundary value problem[formula][formula]wherefis either φ-superlinear or φ-sublinear at ∞ andf(t,0) may be negative andpis a positive continuous function. The results extend several known results for semilinear equations. Our approach is based on fixed point theory for completely continuous operators which leave invariant a suitable cone in a Banach space of continuous functions

Diffusive logistic equation with non-linear boundary conditions

AbstractWe analyze the solutions of a population model with diffusion and logistic growth. In particular, we focus our study on a population living in a patch, Ω⊆Rn with n⩾1, that satisfies a certain non-linear boundary condition and on its survival when constant yield harvesting is introduced. We establish our existence results by the method of sub-super solutions

The Study and Efficacy of Conventional Machine Learning Strategies for Predicting Cardiovascular Disease

Regarding medical science, cardiovascular disease is the main cause of death. Testing patient samples for cardiac disease can save lives and lower mortality rates. During a subsequent visit, the right remedies should be outlined and prescribed. One of the most important factors in preemptive cardiac disease diagnosis is accuracy. Based on this factor, many research approaches were examined and compared. According to the analysis of these approaches, new procedures appear to be more advanced and reliable in detecting cardiac illness. A notation of the methods and their underlying themes and precision levels will be discussed. This paper surveys many models that use these methods and methodologies and evaluates their performance. Models created utilizing supervised learning methods, such as Support Vector Machines (SVM), K-Nearest Neighbour (KNN), Decision Trees (DT), Random Forest (RF), and Logistic Regression Units, are highly valued by researchers. For benchmark datasets like the Cleveland or Kaggle, the methodologies are derived from data mining, machine learning, deep learning, and other related techniques and technologies. The accuracy of the provided methods is graphically demonstrated

Digital Transformation in Insurance Sector

New technologies allow for a significant increase in efficiency, effectiveness and a reduction of costs. The life insurance industry in India has undergone massive changes since 2000 when the industry was liberalized. The future looks interesting for the industry with changes in the way business is conducted and the customer-friendly measures that have been put in place. Due to new entrants, changing consumer behaviors, and technological innovations need to innovate new business model in insurance. These papers discuss how insurers can use the digitization opportunity to deliver greater value to their customers and gain a competitive advantage. Insurers can engage more intensely with existing customers and attract newer customers with innovative products, improve both profitability and growth

Positive Solution Curves of Semipositone Problems with Concave Nonlinearities

We consider the positive solutions to the semilinear equation: -Δu(x) = λf(u(x)) for x ∈ Ω u(x) = 0 for x ∈ ∂Ω where Ω denotes a smooth bounded region in RN (N \u3e 1) and λ \u3e 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) \u3c 0 (semipositone). Assuming that f\u27(∞) ≡ lim t→∞ f\u27(t) \u3e 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)\u27. When Ω is a ball, we determine the exact number of positive solutions for each λ \u3e 0. We also obtain the geometry of the branches of positive solutions completely and establish how they evolve. This work extends and complements that of [3, 7] where f\u27(∞) ≤ 0

MENTHA PIPERITA LINN: PHYTOCHEMICAL, ANTIBACTERIAL AND DIPTERIAN ADULTICIDAL APPROACH

Objective: There is an immense need to develop an alternative antimicrobial source for the treatment of several infectious diseases and restrict its vectors. So, evaluation of phytochemicals from Mentha piperita, its antibacterial and adulticidal potential was undertaken in the present study.Methods: The organic solvent of ethanol and water were used for the preparation of extract for the study. These extracts were analyzed for the qualitative and quantitative phytochemicals. Antimicrobial activity was determined by using agar well diffusion method, and Bioassay was carried out by "Sugar Bait" Method to check adulticidal potential. Results: The Mentha piperita were found a rich source of phytochemical compounds like diterpenes, steroids, tannin, flavonoids, cardial glycosides, alkaloids, phenols, coumarin, and saponin. Both the extracts possesses active antibacterial compounds which shown antibacterial activity. The aqueous (5% of 50 µl) and ethanolic (5% of 100 µl) extract (EA) were found as effective concentration. Salmonella typhimurium showed resistance against both the extracts. The aqueous extract (AE) has found with effective adulticidal potential. Hence it can be used to control and repel most popular disease spreading Dipterian vector, Musca domestica.Conclusion: These results confirm the presence of antibacterial, adulticidal compounds in Mentha piperita which gives an opportunity to explore the possible usage of Mentha piperita in the development of antibiotics and insecticides.Keywords: Mentha piperita L., Phytochemical analysis, Antibacterial, Adulticidal potentia

Novel Protocol for Synthesis of O,O-Dialkyl Monothiophospharic Acid Sodium Salt

Preparation of&nbsp;O,O-dialkyl monothiophospharic acid sodium salt (DMP-SNa) by addition of sulphur selectively on phosphorous using organic base to form a salt of&nbsp;O,O-dialkyl monothiophospharic acid trialkyl amine salt which is soluble in the non-polar organic solvent and treated with alkali to form&nbsp;O,O-dialkyl monothiophospharic acid sodium salt (DAP-SNa). Trialkylamine becomes free and remains in the nonpolar solvents can be recycled. This synthesis method is effluent free. DOI:&nbsp;http://dx.doi.org/10.17807/orbital.v13i5.159