In this paper, we investigate the existence of positive solutions to a second-order Sturm–Liouville boundary-value problem with impulsive effects. The ideas involve differential inequalities and variational methods.

/pdf/applications-of-variational-methods-to-boundary-value-3uzwel9480.pdf

Applications of variational methods to boundary-value problem for impulsive differential equations

In this paper, we consider the existence of solutions for a class of three-point boundary value problems involving nonlinear impulsive fractional differential equations. By use of Banach's fixed point theorem and Schauder's fixed point theorem, some existence results are obtained.

Existence results for the three-point impulsive boundary value problem involving fractional differential equations

Multiple positive solutions for the one-dimensional p -Laplacian

/pdf/multiplicity-of-positive-radial-solutions-for-an-elliptic-2w4n98qi6u.pdf

Multiplicity of positive radial solutions for an elliptic system on an annulus

Based on the relation between Leray–Schauder degree and a pair of strict lower and upper solutions, we focus on the bifurcation analysis for a singular differential system with two parameters, explicit bifurcation points for relative parameters are obtained by using the property of solution for the akin systems and topological degree theory.

/pdf/bifurcation-analysis-for-a-singular-differential-system-with-10ty5w6388.pdf

Bifurcation analysis for a singular differential system with two parameters via to topological degree theory

/pdf/a-multiplicity-result-for-periodic-solutions-of-higher-order-26bc0k08fq.pdf

A multiplicity result for periodic solutions of higher order ordinary differential equations via the method of upper and lower solutions

This work is concerned with the global existence and nonexistence of solutions for a quasilinear parabolic equation with null Dirichlet boundary condition. Based on the Galerkin approximation technique and the theory of a family of potential wells, we obtain the invariant sets and vacuum isolating of global solutions including critical case, and we also give global nonexistence.

/pdf/global-existence-and-nonexistence-of-solutions-for-42pv1rlskg.pdf

Global existence and nonexistence of solutions for quasilinear parabolic equation

In this article, we consider the global bifurcation result and existence of solutions for the following general Laplacian problem, � −(φ(u � (t))) � = λψ(u(t)) + f(t,u, λ), t ∈ (0,1), u(0) = u(1) = 0, (P)

Global bifurcation results for general Laplacian

In this paper we extend primal-dual interior point algorithm for linear optimization(LO) problems to P*(κ) linear complementarity problems(LCPs) ([?]). We define proximity functions and search directions based on kernel functions, Ψ(t) = t p+1 -1/p+1 log t, p ∈ [0,1], which is a generalized form of the one in [?]. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for P*(κ) LCPs. We show that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for P*(κ) LCPs have O((1+2κ)nlogn/c) complexity which is similar to the one in [?]. For small-update methods, we have 0((1+2κ)√nlog n/c) which is the best known complexity so far.

New complexity analysis of ipm for p *(k) lcp based on kernel functions

In this work, we study the regularity of positive solutions for nonlinear fractional differential equation with a singular weight. We define the new Banach space and use this space to show the regularity. We also give an example with a singular weight which may not be in L1. MSC (2010): 34B15, 34B18, 34B27

Regularity of solutions for singular fractional differential equation

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