Decaying positive global solutions of second order difference equations with mean curvature operator

A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is examined by proving new Sturm comparison theorems for linear difference equations and using a fixed point approach based on a linearization device. The process of discretization of the boundary value problem on the unbounded domain is examined, and some discrepancies between the discrete and the continuous cases are pointed out, too

ON HIGHER ORDER NONLINEAR IMPULSIVE BOUNDARY VALUE PROBLEMS

This work studies some two point impulsive boundary value problems composed by a fully differential equation, which higher order contains an increasing homeomorphism, by two point boundary conditions and impulsive e ects. We point out that the impulsive conditions are given via multivariate generalized functions, including impulses on the referred homeomorphism. The method used apply lower and upper solutions technique together with xed point theory. Therefore we have not only the existence of solutions but also the localization and qualitative data on their behavior. Moreover a Nagumo condition will play a key role in the arguments

Multiple Positive solutions of a (p1,p2)(p_1,p_2)-Laplacian system with nonlinear BCs

Using the theory of fixed point index, we discuss existence, non-existence, localization and multiplicity of positive solutions for a $(p_1,p_2)$-Laplacian system with nonlinear Robin and/or Dirichlet type boundary conditions. We give an example to illustrate our theory.Comment: arXiv admin note: text overlap with arXiv:1408.017

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)

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

Quasilinear fractional differential equation with resonance boundary condition

In this paper, we consider quasilinear fractional differential equation with resonance boundary condition. After translating the quasilinear equation into the linear fractional differential system, by using coincidence degree theory, the existence result is established

Decaying positive global solutions of second order difference equations with mean curvature operator

A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is examined by proving new Sturm comparison theorems for linear difference equations and using a fixed point approach based on a linearization device. The process of discretization of the boundary value problem on the unbounded domain is examined, and some discrepancies between the discrete and the continuous cases are pointed out, too

Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x’(t))]’ involved with the function ρ, which makes the solutions un-concave