Infinitely many solutions for a Dirichlet boundary value problem depending on two parameters

In this paper, using Ricceri\u27s variational principle, we prove the existence of infinitely many weak solutions for a Dirichlet doubly eigenvalue boundary value problem

Infinitely many weak solutions for fourth-order equations depending on two parameters

In this paper, by employing Ricceri variational principle, we prove the existence of infinitely many weak solutions for fourth-order problems depending on two real parameters. We also provide some particular cases and a concrete example in order to illustrate the main abstract results of this paper

Positive solutions for a class of infinite semipositone problems involving the p-Laplacian operator

We discuss the existence of a positive solution to a given infinite semipositone problem

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic

Nontrivial solutions for nonlinear algebraic systems via a local minimum theorem for functionals

In this article, we use a critical point theorem (local minimum result) for differentiable functionals to prove the existence of at least one nontrivial solution for a nonlinear algebraic system with a parameter. Our goal is achieved by requiring an appropriate asymptotic behavior of the nonlinear term at zero. Some applications to discrete equations are also presented

Existence of positive solutions for p(x)-Laplacian problems

We consider the system of differential equations $$displaylines{ -Delta_{p(x)} u=lambda [g(x)a(u) + f(v)] quadhbox{in }Omegacr -Delta_{q(x)} v=lambda [g(x)b(v) + h(u)] quadhbox{in }Omegacr u=v= 0 quadhox{on } partial Omega }$$ where $p(x) in C^1(mathbb{R}^N)$ is a radial symmetric function such that $sup| abla p(x)| < infty$, $1 < inf p(x) leq sup p(x) < infty$, and where $-Delta_{p(x)} u = -{ m div}| abla u|^{p(x)-2} abla u$ which is called the $p(x)$-Laplacian. We discuss the existence of positive solution via sub-super-solutions without assuming sign conditions on $f(0),h(0)$

Infinite semipositone problems with indefinite weight and asymptotically linear growth forcing-terms

In this work, we study the existence of positive solutions to the singular problem $$displaylines{ -Delta_{p}u = lambda m(x)f(u)-u^{-alpha} quad hbox{in }Omega,cr u = 0 quad hbox{on }partial Omega, }$$ where $lambda$ is positive parameter, $Omega$ is a bounded domain with smooth boundary, $0 m_0>0$, $|m|_{infty}<infty$. We prove the existence of a positive solution for a certain range of $lambda$ using the method of sub-supersolutions

Existence of solutions for a class of second-order boundary value problems

We employ some known critical point theorems to establish results on the existence of weak solutions for an impulsive boundary value problem depending on two real parameters. One of the results ensures the existence of at least three weak solutions, while another one proves the existence of at least one

Multiple positive solutions for superlinear Kirchhoff type problems on R^N

By using critical point theory, we establish the existence of infinitely many weak solutions for a class of Navier boundary-value problem depending on two parameters and involving the p(x)-biharmonic operator. Under an appropriate oscillatory behaviour of the nonlinearity and suitable assumptions on the variable exponent, we obtain a sequence of pairwise distinct solutions