Infinitely Many Entire Solutions of an Elliptic System with Symmetry

On Silverman's conjecture for a family of elliptic curves

Let $E$ be an elliptic curve over $Bbb{Q}$ with the given Weierstrass equation $ y^2=x^3+ax+b$. If $D$ is a squarefree integer, then let $E^{(D)}$ denote the $D$-quadratic twist of $E$ that is given by $E^{(D)}: y^2=x^3+aD^2x+bD^3$. Let $E^{(D)}(Bbb{Q})$ be the group of $Bbb{Q}$-rational points of $E^{(D)}$. It is conjectured by J. Silverman that there are infinitely many primes $p$ for which $...

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

A Remark on Entire Explosive Solutions for a Class of Elliptic System with Linear Gradient Terms

In this paper, we study the existence of positive entire large radial solutions to the nonlinear elliptic system with gradient terms { div(|∇u|p−2∇u) + |∇u| = m(|x|)f1(v)f2(u), x ∈ RN div(|∇v|q−2∇v) + |∇v| = n(|x|)g1(v)g2(u), x ∈ RN (1) The nonlinearities fi, gi (i = 1, 2) are positive and continuous, while the potentials m, n are continuous and certain growth condition. We give some simple con...

Existence results of infinitely many solutions for a class of p(x)-biharmonic problems

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.