We investigate existence and nonexistence of solutions for NP-hard equations involving absolute values of variables: Ax − |x| = b, where A is an arbitrary n × n real matrix. By utilizing an equivalence relation to the linear complementarity problem (LCP) we give existence results for this class of absolute value equations (AVEs) as well as a method of solution for special cases. We also give no...

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

In this paper, first we consider the existence and nonexistence of Einstein metrics on the topological 4-manifolds 3CP#kCP, the connected sum of CP with both choices of orientation, by using the idea of Răsdeaconu–Şuvaina, 2009, and the constructions in Park–Park– Shin, 2013. Then, we study the existence or nonexistence of nonsingular solutions of the normalized Ricci flow on the exotic smooth ...

Abstract We revisit the liquid drop model with a general Riesz potential. Our new result is existence of minimizers for conjectured optimal range parameters. also prove conditional uniqueness and nonexistence heavy nuclei.

In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on ...

‎In this paper‎, ‎we formulate the sixth-order boundary value problem as Fredholm integral equation by finding Green's function and obtain the sufficient conditions for existence and multiplicity of positive solution for this problem‎. ‎Also nonexistence results are obtained‎. ‎An example is given to illustrate the results of paper‎.

We consider the initial value problem for the reaction-diffusion equation ut = ∆u + f(u). In this paper we show the existence and nonexistence of the global solutions in time. Especially, we extend the condition of the nonlinear terms to more general. We have the results of the existence and the nonexistence for the equation with the nonlinear term f satisfying lim infs→0 f(s)/sp > 0 and lim su...