Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques.     

Regioselective carbolithiation of o-amino-(E)-stilbenes: cascade route to the quinoline scaffold

[reaction: see text] The regioselective carbolithiation of substituted ortho-amino-(E)-stilbenes can be exploited to initiate cascade reaction sequences that can be utilized as new routes to substituted 3,4-dihydro-1H-quinolin-2-ones, 1,2,3,4-tetrahydroquinolines, 1,4-dihydroquinolines, and quinolines.     

Differential mixed variational inequalities in finite dimensional spaces

In this paper, we introduce and study a class of differential mixed variational inequalities in finite dimensional Euclidean spaces. Under various conditions, we obtain linear growth and bounded linear growth of the solution set for the mixed variational inequalities. Moreover, we present some conclusions which enrich the literature on the mixed variational inequalities and generalize the corresponding results of [4]. In particular we prove existence theorems for weak solutions of a differential mixed variational inequality in the weak sense of Carathéodory by using a result on differential inclusions involving an upper semicontinuous set-valued map with closed convex values. Also by employing the results from differential inclusions we establish a convergence result on Euler time-dependent procedure for solving initial-value differential mixed variational inequalities.     

Random and deterministic fixed point theory for generalized contractive maps

Fixed point and homotopy results are presented for generalized contractions on complete gauge spaces. In addition we obtain random fixed point results for generalized contractions.     

Viable solutions of differential inclusions on closed sets

This article studies the existence of viable solutions to the Cauchy problem u′ ∈ ? (t , u) for a.e. t∈ [0,1], u (0)=x ₀ ∈ K (a closed subset of R ^N ) where the nonlinearity ? satisfies a Wintner-type growth condition.     

Existence of subharmonic solutions and homoclinic orbits for a class of even higher order differential equations

Using the variational structure and the Z ₂ group index theory we establish the existence of subharmonic solutions and homoclinic solutions for a class of even higher order differential equation.     

Positive solutions for singular boundary value problems with sign changing nonlinearities depending on x′ via index theory

Using the theory of fixed point index, this article discusses the existence of positive solutions for singular second-order boundary value problems, where f may be singular at x?=?0 and x′=0, and f may change sign.     

Generalized contractions in partially ordered metric spaces

We present some fixed point results for monotone operators in a metric space endowed with a partial order using a weak generalized contraction-type assumption.     

An intersection theorem for set-valued mappings

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ? X, S: Y ? X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.