A new proof of Dávila–Flores–Guerra’s result on existence of singular solutions

Here we give a self-contained new proof of the existence of singular solutions to a class Dirichlet problem with a singular nonlinearity. These results were obtained by Dávila–Flores–Guerra (Dávila et al., 2009). Our proof is much more direct and simpler.     

Quasi-variational problems with non-self map on Banach spaces: Existence and applications

This paper focuses on the analysis of generalized quasi-variational inequality problems with non-self constraint map. To study such problems, in Aussel et al. (2016) the authors introduced the concept of the projected solution and proved its existence in finite-dimensional spaces. The main contribution of this paper is to prove the existence of a projected solution for generalized quasi-variational inequality problems with non-self constraint map on real Banach spaces. Then, following the multistage stochastic variational approach introduced in Rockafellar and Wets (2017), we introduce the concept of the projected solution in a multistage stochastic setting, and we prove the existence of such a solution. We apply this theoretical result in studying an electricity market with renewable power sources.     

Nontrivial solutions of some fractional problems

In this paper, we study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet boundary data, in presence of a superlinear term. Starting from the well-known Ambrosetti–Rabinowitz condition, we consider different growth assumptions on the nonlinearity, all of superlinear type. Furthermore, we give an extension of Ambrosetti–Rabinowitz condition, a non-Ambrosetti–Rabinowitz condition and apply to study the fractional Laplacian equation. We obtain some different existence results in this setting by using Fountain Theorem. Our results are extension of some problems studied by Bisci et al. (2016) and Binlin et al. (2015).     

Strategic absentmindedness in finitely repeated games

In this paper we consider finitely repeated games in which players can unilaterally commit to behave in an absentminded way in some stages of the repeated game. We prove that the standard conditions for folk theorems can be substantially relaxed when players are able to make this kind of compromises, both in the Nash and in the subgame perfect case. We also analyze the relation of our model with the repeated games with unilateral commitments studied, for instance, in García-Jurado et al. (Int. Game Theory Rev. 2:129–139, 2000). Authors acknowledge the financial support of Ministerio de Educaci ón y Ciencia, FEDER and Fundación Séneca de la Región de Murcia through projects SEJ2005-07637-C02-02, ECO2008-03484-C02-02, MTM2005-09184-C02-02, MTM2008-06778-C02-01 and 08716/PI/08.     

几类具Pucci算子的椭圆方程组解的存在性

研究完全非线性椭圆方程组解的存在性问题,其中ΩR~n,n≥2是有界光滑区域,—Μ_(λ,Λ)~+为具参数0<λ≤Λ的Pucci算子.首先,对f_i,i=1,2为一致有界函数的情形,证明了此方程组存在有界非负解.其次,当{f_1,f_2}是拟增的,且方程组存在有序上、下解时,利用上、下解方法,并结合增算子的不动点定理证明了此方程组存在最大非负解和最小非负解.当{f_1,f_2}是拟减或混拟单调时,使用Schauder不动点定理证明了此方程组至少存在一个非负解.针对此方程组中f_i,i=1,2的某些特殊形式,证明了相应方程组正解的存在性.最后给出了应用实例.     

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.     

Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Díaz-Ramos, García-Río and Vázquez-Lorenzo (J. Geom. Anal. 16, 39–52, 2006). Work begun during the author’s visit to the University of Santiago de Compostela, supported by Grant MTM2006-01432 (Spain).     

On the 4-color theorem for signed graphs

Máčajová et al. (2016) defined the chromatic number of a signed graph which coincides for all-positive signed graphs with the chromatic number of unsigned graphs. They conjectured that in this setting, for signed planar graphs four colors are always enough, generalizing thereby The Four Color Theorem. We disprove the conjecture.     

Multiple Nontrivial Solutions for a Class of p-Laplacian Equations

In this paper a class of p-Laplacian equations are considered. The existence of five nontrivial solutions is stated. By the standard supersolution and subsolution method, we prove the existence of minimal positive solution and maximal negative solution in L ^∞(Ω). Furthermore, in virtue of the well-known Mountain-Pass Theorem and Second Deformation Theorem, we can give additional three nontrivial solutions, i.e., one positive solution, one negative solution and one sign-changing solution.     

A bifurcation problem governed by the boundary condition I

We deal with positive solutions of Δu = a(x)u ^p in a bounded smooth domain subject to the boundary condition ∂u/∂v = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ₁ where, roughly speaking, σ₁ is finite if and only if |∂Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile of the solution as λ → σ₁. Supported by DGES and FEDER under grant BFM2001-3894 (J. García-Melián and J. Sabina) and ANPCyT PICT No. 03-05009 (J. D. Rossi). J.D. Rossi is a member of CONICET.     

Global solution to the n-dimensional non-resistive MHD system with damping in magnetic field

The global existence is obtained for the solution to the viscous non-resistive MHD system with magnetic damping in ${\mathbb{R}}^n(n\ge 2)$. This study is inspired by the recent examinations obtained by Fefferman et al. (2014) and Chemin et al. (2016) on the local well-posedness of the viscous non-resistive MHD system.     

A new approach to relative asymptotic behavior for discrete Sobolev-type orthogonal polynomials on the unit circle

In Foulquié et al. (1999) [2], Li and Marcellán (1996) [4], Marcellán and Moral (2002) [5], the relative asymptotic behavior of orthogonal polynomials with respect to a discrete Sobolev-type inner product on the unit circle was studied. In this paper, we propose an alternative approach to this problem based on the Uvarov spectral transformation.     

Solitary waves for the Klein-Gordon-Maxwell system with critical exponent

In this paper we study the existence of solutions for nonlinear Klein-Gordon-Maxwell equations coupled with Maxwell’s equations when the nonlinearity exhibits critical growth. We improve some previous existence results in Azzollini et al. (2009) [5], Carrião et al. (2009) [4] and Cassani (2004) [3].     

Optimal portfolio selection for general provisioning and terminal wealth problems

In Dhaene et al. (2005), multiperiod portfolio selection problems are discussed, using an analytical approach to find optimal constant mix investment strategies in a provisioning or a savings context. In this paper we extend some of these results, investigating some specific, real-life situations. The problems that we consider in the first section of this paper are general in the sense that they allow for liabilities that can be both positive or negative, as opposed to Dhaene et al. (2005), where all liabilities have to be of the same sign. Secondly, we generalize portfolio selection problems to the case where a minimal return requirement is imposed. We derive an intuitive formula that can be used in provisioning and terminal wealth problems as a constraint on the admissible investment portfolios, in order to guarantee a minimal annualized return. We apply our results to optimal portfolio selection.     

A numerical algorithm for a class of BSDEs via the branching process

We give a study to the algorithm for semi-linear parabolic PDEs in Henry-Labordère (2012) and then generalize it to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren et al. (to appear)  [5] and extended in Ekren et al. (2012)   and .     

Nonlinear partial differential systems on Riemannian manifolds with their geometric applications

We make the first study of how the existence of (essential) positive supersolutions of nonlinear degenerate partial differential equations on a manifold affects the topology, geometry, and analysis of the manifold. For example, for surfaces in R³ we prove a Bernstein-type theorem that generalizes and unifies three distinct theorems. In higher dimensions, we provide topological obstructions for a minimal hypersurface in Rⁿ⁺¹ to admit an essential positive supersolution. This immediately yields information about the Gauss map of complete minimal hypersurfaces in Rⁿ⁺¹. By coping with a wider class of nonlinear partial differential equations that are involved with (p)-harmonic maps and (p)-superstrongly unstable manifolds, we derive information on the regularity of minimizers, homotopy groups, and solutions to Dirichlet problems, from the existence of essential positive supersolutions.     

Large deviations for estimators of unknown probabilities, with applications in risk theory

We present large deviation results for estimators of unknown probabilities which satisfy a suitable exponential decay condition. These results provide some extensions of the large deviation estimates given in Macci and Petrella (2006). Furthermore we propose a classical approach which is different from the one presented in Ganesh et al. (1998) and we cannot say that the Bayesian approach is more conservative as in that paper.     

Existence and global stability of traveling curved fronts in the Allen-Cahn equations

This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front.     

On the Lovász theta function and some variants

The Lovász theta function of a graph is a well-known upper bound on the stability number. It can be computed efficiently by solving a semidefinite program (SDP). Actually, one can solve either of two SDPs, one due to Lovász and the other to Grötschel et al. The former SDP is often thought to be preferable computationally, since it has fewer variables and constraints. We derive some new results on these two equivalent SDPs. The surprising result is that, if we weaken the SDPs by aggregating constraints, or strengthen them by adding cutting planes, the equivalence breaks down. In particular, the Grötschel et al. scheme typically yields a stronger bound than the Lovász one.     

On the minimal Keller–Segel system with logistic growth

This paper applies a delicate method which is inspired by Deuring (1987) and is different from those of Winkler (2010) and Yang et al. (2015) to show the known conclusion: The weak chemotactic effect can ensure the global existence and boundedness of the solutions of the minimal Keller–Segel model with logistic growth in any dimensional cases. Moreover, we obtain the explicit uniform-in-time upper bound for the global solution. It is noted that the method used in the paper may be employed to study other chemotaxis systems.