On optimal taxes and subsidies: A discrete saddle-point theorem with application to job matching under constraints

When a government intervenes in markets by setting a target amount of goods/services traded, its tax/subsidy policy is optimal if it entices the market participants to obey the policy target while achieving the highest possible social welfare. For the model of job market interventions by Kojima et al. (2019), we establish the existence of optimal taxes/subsidies as well as their characterization. Our methodological contribution is to introduce a discrete version of Karush-Kuhn-Tucker's saddle-point theorem based on the techniques in discrete convex analysis. We have two main results: we (i) characterize the optimal taxes/subsidies and the corresponding equilibrium salaries as the minimizers of a Lagrange function, and (ii) prove that the function satisfies a notion of discrete convexity (called L#-convexity). These results together with others imply that an optimal tax/subsidy level exists and can be calculated via a computationally efficient algorithm.

Some existence theorems for semilinear Neumann problems with Landesman-Lazer condition revisited

In this paper, existence theorems are established for Neumann problems for semilinear elliptic equations at resonance together with Landesman-Lazer condition revisited. Our existence results follow as an application of the Saddle point Theorem together with a standard eigenspace decomposition.

Existence of periodic solutions of fourth-order p-Laplacian difference equations

By making use of the critical point theory, the existence of periodic solutions for fourth-order nonlinear p-Laplacian difference equations is obtained. The main approach used in our paper is a variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions of fourth-order nonlinear p-Laplacian difference equations. The results obtained successfully generalize and complement the existing one.

Existence and multiplicity of solutions for class of Navier boundary $p$-biharmonic problem near resonance

This paper studies the existence and multiplicity of weak solutions for the following elliptic problem\\$\Delta(\rho|\Delta u|^{p-2}\Delta u)=\lambda m(x)|u|^{p-2}u+f(x,u)+h(x)$ in $\Omega,$\\$u=\Delta u=0$ on $\partial\Omega.$By using Ekeland's variationalprinciple, Mountain pass theorem and saddle point theorem, theexistence and multiplicity of weak solutions are established.

Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.