Existence and location results for hinged beam equations with unbounded nonlinearities

This work presents some existence, non-existence and location results for the problem composed by the fourth-order fully nonlinear equation u^4(x)= f(x,u(x),u'(x),u''(x),u'''(x))+ sp(x) for x in [0; 1], where f and p are continuous functions and s is a real parameter, with the Lidstone boundary conditions u(0)= u(1)=u''(0)=u''(1)=0. This problem models several phenomena, such as, the bending of an elastic beam simply supported at the endpoints. The arguments used apply a lower and upper solutions technique, a priori estimations and topological degree theory. In this paper we replace the usual bilateral Nagumo condition by some one-sided conditions, which enables us to consider unbounded nonlinearities

A note on a class of problems for a higher-order fully nonlinear equation under one-sided Nagumo-type condition

The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation u⁽ⁿ⁾(t)=f(t,u(t),u′(t),…,u⁽ⁿ⁻¹⁾(t)), n≥2, with the boundary conditions u^{(i)}(a) = A, for i=0,⋯,n-3, u⁽ⁿ⁻¹⁾(a) = B, u⁽ⁿ⁻¹⁾(b)=C or u^{(i)}(a)=A, for i=0,⋯,n-3, c₁u⁽ⁿ⁻²⁾(a)-c₂u⁽ⁿ⁻¹⁾(a)=B, c₃u⁽ⁿ⁻²⁾(b)+c₄u⁽ⁿ⁻¹⁾(b)=C, with A_{i},B,C∈R, for i=0,⋯,n-3, and c₁, c₂, c₃, c₄ real positive constants. It is assumed that f:[a,b]×Rⁿ⁻¹→R is a continuous function satisfying one-sided Nagumo-type conditions which allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on Leray-Schauder topological degree and lower and upper solutions method

Homoclinic and periodic solutions for a class of second order differential equations

In this paper we are concerned with the existence of positive homoclinic solutions of the second order equation …info:eu-repo/semantics/publishedVersio

Coupled systems with Ambrosetti-Prodi-type differential equations

In this paper, we consider some boundary value problems composed by coupled systems of second-order differential equations with full nonlinearities and general functional boundary conditions verifying some monotone assumptions. The arguments apply the lower and upper solutions method, and defining an adequate auxiliary, homotopic, and truncated problem, it is possible to apply topological degree theory as the tool to prove the existence of solution. In short, it is proved that for the parameter values such that there are lower and upper solutions, then there is also, at least, a solution and this solution is localized in a strip bounded by lower and upper solutions. As far as we know, it is the first paper where Ambrosetti-Prodi differential equations are considered in couple systems with different parameters

SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results

Locally Expansive Solutions for a Class of Iterative Equations

Iterative equations which can be expressed by the following form ( ) = ( , ( ), 2 ( ), . . . , −1 ( )), where ≥ 2, are investigated. Conditions for the existence of locally expansive 1 solutions for such equations are given

Os babuínos da Guiné (Papio papio) na Guiné-Bissau: Uma revisão bibliográfica para a conservação da espécie

O babuíno da Guiné (Papio papio), que é simultaneamente a espécie de babuínos mais ameaçada e a menos investigada, foi reportado como estando a diminuir na Guiné-Bissau devido à intensa pressão exercida pelas atividades antropogénicas. Estes resultados motivaram investigação dirigida à biologia, ecologia evolução, parasitologia e conservação das populações da espécie na Guiné Bissau, para melhorar o conhecimento e a conservação dos babuínos da Guiné. A população da Guiné-Bissau destaca-se de outras por uma composição genética diferenciada. As populações do sul do país, em contacto frequente com atividades antropogénicas, demonstram modificações comportamentais e poderão estar ameaçadas por interações negativas com as comunidades humanas locais. A conservação dos babuínos da Guiné deverá ser ativamente gerida para evitar o desaparecimento silencioso e não notado de populações.info:eu-repo/semantics/publishedVersio

Existence result for some third order separated boundary value problems

This work presents an existence result for the third order separated boundary value problem … We apply for the above third order problem the lower and upper solution method, following some arguments by [4] and [3] to study some second order separated boundary value problems ….info:eu-repo/semantics/publishedVersio