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

Solvability for second-order nonlocal boundary value problems with a p-Laplacian at resonance on a half-line

This paper investigates the solvability of the second-order boundary value problems with the one-dimensional $p$-Laplacian at resonance on a half-line $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'=f(t,x(t),x'(t)),~~~~0<t<\infty,\\ x(0)=\sum\limits_{i=1}^{n}\mu_ix(\xi_{i}), ~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right.$$ and $$\left\{\begin{array}{llll} (c(t)\phi_{p}(x'(t)))'+g(t)h(t,x(t),x'(t))=0,~~~~0<t<\infty,\\ x(0)=\int_{0}^{\infty}g(s)x(s)ds,~~\lim\limits_{t\rightarrow +\infty}c(t)\phi_{p}(x'(t))=0 \end{array}\right.$$ with multi-point and integral boundary conditions, respectively, where $\phi_{p}(s)=|s|^{p-2}s$, $p>1$. The arguments are based upon an extension of Mawhin's continuation theorem due to Ge. And examples are given to illustrate our results

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

A boundary value problem on the half-line for superlinear differential equations with changing sign weight

The existence of positive solutions x for a superlinear differential equation with p-Laplacian is here studied, satisfying the boundary conditions x(0) = x(∞) = 0. Under the assumption that the weight changes its sign from nonpositive to nonnegative, necessary and sufficient conditions for the existence are derived by combining Kneser-type properties for solutions of an associated boundary value problem on a compact set, a-priori bounds for solutions of suitable boundary value problems on noncompact intervals, and continuity 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

Positive solutions for singular ϕ−\phi-Laplacian BVPs on the positive half-line

In this work, we are concerned with the existence of positive solutions for a $\phi$ Laplacian boundary value problem on the half-line. The results are proved using the fixed point index theory on cones of Banach spaces and the upper and lower solution technique. The nonlinearity may exhibit a singularity at the origin with respect to the solution. This singularity is treated by regularization and approximation together with compactness and sequential arguments