Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear elliptic problems

In this paper we consider the following problem

(?)     

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

In this paper we consider the problem

(P)     

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

We study the fully nonlinear elliptic equation

(0.1)     

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)     

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

Consider the equation

(0.1)     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

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)     

Asymptotically self-similar solutions of the damped wave equation

We consider the damped hyperbolic equation

(1)     

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

(∗)     

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

     

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:

(∗)     

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

We consider the following Cauchy problem with a singular nonlinearity

(P)

     

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

For the two-phase membrane problem

     

Asymptotically linear Schrödinger equations with sign-changing potential

In this paper, we show that the following system:

(0.1)     

On the uniqueness of discontinuous solutions to the Degasperis-Procesi equation

We prove uniqueness within a class of discontinuous solutions to the nonlinear and third order dispersive Degasperis-Procesi equation

     

Semilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions

This work deals with the analysis of problems

     

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

     

Multiplicity of solutions to uniformly elliptic fully nonlinear equations with concave-convex right-hand side

We deal with existence, non-existence and multiplicity of solutions to the model problem

(P)     

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)     

Principal eigenvalue of a very badly degenerate operator and applications

In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator