Related papers: Nonclassical Solutions of Fully Nonlinear Elliptic…

The existence of entire solutions to quasilinear elliptic systems exhibiting both singular and convective reaction terms is discussed. An auxiliary problem, obtained by `freezing' the convection terms and `shifting' the singular ones, is…

We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on finding conformal Hermitian metrics with prescribed…

This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…

New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…

We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.

We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi-Yau type problems in torus bundles.

We obtain comparison theorems for non-negative solutions of quasilinear elliptic inequalities

Over many decades fully nonlinear PDEs, and the complex Monge-Amp\`ere equation in particular played a central role in the study of complex manifolds. Most previous works focused on problems that can be expressed through equations involving…

In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.

In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case…

For a certain class of solutions of the cubic nonlinear Sch\"odinger equation we prove non-existence in the generic case. In the nongeneric case we present a two-parameter set of solutions, bounded or unbounded, depending on corresponding…

We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and…

We obtain an explicit H\"older regularity result for viscosity solutions of a class of second order fully nonlinear equations leaded by operator that are neither convex/concave nor uniformly elliptic.

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational,…

In this paper, we establish a priori estimates for solutions of a general class of fully non-linear equations on compact almost Hermitian manifolds. As an application, we solve the complex Hessian equation and the Monge--Amp\`ere equation…

This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…

In this article we study the existence and uniqueness of solutions of stochastic continuity equation with irregular coefficients.

We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We announce…

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…