Relaxed penalty at infinity for semilinear elliptic equations

Semilinear Elliptic Equations Having Asymptotic Limits at Zero and Infinity

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Nontrivial solutions of elliptic semilinear equations at resonance

We find nontrivial solutions for semilinear boundary value problems having resonance both at zero and at infinity.

Nonexistence of Nonconstant Global Minimizers with Limit at ∞ of Semilinear Elliptic Equations in All of Rn

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation −∆u = f(u) in the whole R , where f ∈ C(R) is a general nonlinearity and N ≥ 1 is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

Asymptotic behavior of solutions of semilinear elliptic equations in unbounded domains: two approaches

In this paper, we study the asymptotic behavior as x1 → +∞ of solutions of semilinear elliptic equations in quarteror half-spaces, for which the value at x1 = 0 is given. We prove the uniqueness and characterize the one-dimensional or constant profile of the solutions at infinity. To do so, we use two different approaches. The first one is a pure PDE approach and it is based on the maximum prin...