Elliptic problems with nonlinear terms depending on the gradient and singular on the boundary

In this paper we consider the problem

(P)     

Positive solutions of asymptotically linear Schrödinger-Poisson systems with a radial potential vanishing at infinity

In this paper, we study the Schrödinger-Poisson system

(SP)     

On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

Asymptotically self-similar solutions of the damped wave equation

We consider the damped hyperbolic equation

(1)     

Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear elliptic problems

In this paper we consider the following problem

(?)     

The Fujita exponent for semilinear heat equations with quadratically decaying potential or in an exterior domain

Consider the equation

(0.1)     

Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations

We study the fully nonlinear elliptic equation

(0.1)     

Existence and regularity of nonnegative solution of a singular quasi-linear anisotropic elliptic boundary value problem with gradient terms

In this paper, we consider the singular quasi-linear anisotropic elliptic boundary value problem

(P)     

Neumann problem for the Korteweg-de Vries equation

We consider Neumann initial-boundary value problem for the Korteweg-de Vries equation on a half-line

(0.1)     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

The existence and decay of solutions of a damped Kirchhoff-Carrier equation in Banach spaces

This paper is concerned with the study of the existence and decay of solutions of the following initial value problem:

(∗)     

Asymptotically linear Schrödinger equations with sign-changing potential

In this paper, we show that the following system:

(0.1)     

Convergence to steady states in a viscous Hamilton-Jacobi equation with degenerate diffusion

This paper deals with weak solutions of the one-dimensional viscous Hamilton-Jacobi equation

     

Hausdorff measure and stability for the p-obstacle problem (2<p<∞)

In this paper we analyze the free boundary for the inhomogeneous obstacle problem with zero obstacle governed by the degenerate operator

     

Single and multi-peak solutions for a nonlinear Maxwell-Schrödinger system with a general nonlinearity

For the following elliptic system in R³

     

On the Cauchy problem for a coupled system of third-order nonlinear Schrödinger equations

We investigate some well-posedness issues for the initial value problem (IVP) associated with the system

     

The two-phase membrane problem—An intersection-comparison approach to the regularity at branch points

For the two-phase membrane problem

     

Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption

We consider the Cauchy problem for the damped wave equation with absorption

(∗)     

Positive solutions for infinite semipositone problems with falling zeros

We consider the positive solutions to the singular problem

(P)     

Boundedness and finite-time collapse in a chemotaxis system with volume-filling effect

We consider the elliptic-parabolic PDE system