This paper studies a four-field hyperbolic PDE model that was recently introduced by Bemfica, Disconzi, and Noronha for the pure radiation fluid with viscosity, asks whether shock waves admit continuous profiles in this description. The containing two free parameters $\ensuremath{\mu}$, $\ensuremath{\nu}$ being causal whenever one chooses $(\ensuremath{\mu},\ensuremath{\nu})$ from certain range...

Abstract In this article, the existence and nonexistence of solutions for quasilinear elliptic equations involving multiple critical terms under Dirichlet boundary conditions on bounded smooth domains Ω ⊂ R N ...

In this paper we study existence of positive solutions to singular elliptic boundary value problems involving divergence terms in general domains. By constructing suitable upper and lower solutions and making comparison, we obtain suucient conditions for existence and nonexistence of solutions. We also study a concrete example to show that the conditions imposed on parameters appearing in the s...

We discuss the existence of breather solutions for a Discrete Nonlinear Schrödinger equation in an infinite N-dimensional lattice, involving site dependent anharmonic parameter. We give a simple proof on the existence of (nontrivial) breather solutions based on variational approach, assuming that the sequence of anharmonic parameters is in an appropriate sequence space (decays with an appropria...

This paper is concerned with optimal control of semilinear stochastic evolution equations on Hilbert space driven by stochastic vector measure. Both continuous and discontinuous (measurable) vector fields are admitted. Due to nonexistence of regular solutions, existence and uniqueness of generalized (or measure valued) solutions are proved. Using these results, existence of optimal feedback con...

In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of posit...