Multiple positive solutions for functional dynamic equations on time scales

AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results

Existence and iteration of monotone positive solutions for third-order nonlocal BVPs involving integral conditions

This paper is concerned with the existence of monotone positive solution for the following third-order nonlocal boundary value problem $u^{\prime \prime \prime }\left(t\right) +f\left( t,u\left( t\right), u^{\prime}\left( t\right)\right) =0,\, 0<t<1$; $u\left( 0\right) =0,$ $au^{\prime}\left( 0\right)-b u^{\prime\prime}\left( 0\right)=\alpha[u],$ $c u^{\prime}\left( 1\right)+d u^{\prime\prime}\left( 1\right)=\beta[u],$ where $f\in C([0,1]\times R^{+}\times R^{+}, R^{+})$, $\alpha[u]=\int_{_{0}}^{1}u(t)dA(t)$ and $\beta[u]=\int_{_{0}}^{1}u(t)dB(t)$ are linear functionals on $C[0,1]$ given by Riemann-Stieltjes integrals. By applying monotone iterative techniques, we not only obtain the existence of monotone positive solution but also establish an iterative scheme for approximating the solution. An example is also included to illustrate the main results

Positive Solutions for Third-Order p

We study the following third-order p-Laplacian functional dynamic equation on time scales: Φp(uΔ∇(t))∇+a(t)f(u(t),u(μ(t)))=0, t∈0,TT,  u(t)=φ(t),  t∈-r,0T,  uΔ(0)=uΔ∇(T)=0, and u(T)+B0(uΔ(η))=0. By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established

A survey on stationary problems, Green's functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions

In this paper, we present a survey of recent results on the Green's functions and on spectrum for stationary problems with nonlocal boundary conditions. Results of Lithuanian mathematicians in the field of differential and numerical problems with nonlocal boundary conditions are described. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)

[Book of abstracts]

USPCAPESCNPqFAPESPICMC Summer Meeting on Differential Equations (2016 São Carlos