Elliptic problems with a Hardy potential and critical growth in the gradient: Non-resonance and blow-up results

In this article we analyze existence and nonexistence of positive solutions to problem

     

A sharp form of an embedding into exponential and double exponential spaces

Let Ω be a bounded domain in . In the well-known paper (Indiana Univ. Math. J. 20 (1971) 1077) Moser found the smallest value of K such that

     

Results for degenerate nonlinear elliptic equations involving a Hardy potential

Consider the problem

     

Adams' inequalities for bi-Laplacian and extremal functions in dimension four

Let Ω⊂R⁴ be a smooth oriented bounded domain, be the Sobolev space, and be the first eigenvalue of the bi-Laplacian operator Δ². Then for any α: 0?α<λ(Ω), we have

     

Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential

We deal with the following parabolic problem

     

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

In this paper we consider the problem

(P)     

On Hamiltonian elliptic systems with periodic or non-periodic potentials

This paper is concerned with the following Hamiltonian elliptic system

     

Sign-changing saddle point

In this paper, the Saddle-point theorems are generalized to a new version by showing that there exists a “sign-changing” saddle point besides zero. The abstract result is applied to the semilinear elliptic boundary value problem

     

Existence and nonexistence of the global solution for the semilinear parabolic system on Riemannian manifold

In this paper, we study the global existence and nonexistence of solutions to the following semilinear parabolic system

     

Nonlinear Liouville theorems for Grushin and Tricomi operators

The aim of this paper is to study necessary conditions for existence of weak solutions of the inequality

     

The minimal period problem for the classical forced pendulum equation

Considered in this paper is the existence/nonexistence of periodic solutions with prescribed minimal periods to the classical forced pendulum equation,

     

Ground state solutions for a periodic Schrödinger equation with superlinear nonlinearities

In this paper we consider the following Schrödinger equation:

     

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

We study spectral properties for HK,Ω, the Krein-von Neumann extension of the perturbed Laplacian −Δ+V defined on , where V is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,r, r>1/2. In particular, in the aforementioned context we establish the Weyl asymptotic formula