On ground state solutions of −Δu = up − uq

New conditions on ground state solutions for Hamiltonian elliptic systems with gradient terms

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

State Bankruptcy from the Ground Up

A computer assisted study of uniqueness of ground state solutions

For the problem (here u = u(x)) ∆u− u + αu + βu = 0, x ∈ R, lim |x|→∞ u(x) = 0 , with constants 1 ≤ p < q < r < n+2 n−2 , and α, β > 0, uniqueness of radial solution (called ground state solution) is not known. We present a procedure, which opens the way to produce computer assisted proofs of uniqueness for specific p, q, r, and n.

new conditions on ground state solutions for hamiltonian elliptic systems with gradient terms

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...