Opening infinitely many nodes

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.

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.

Infinitely Many Solutions for a Steklov Problem Involving the p(x)-Laplacian Operator

By using variational methods and critical point theory for smooth functionals defined on a reflexive Banach space, we establish the existence of infinitely many weak solutions for a Steklov problem involving the p(x)-Laplacian depending on two parameters. We also give some corollaries and applicable examples to illustrate the obtained result../files/site1/files/42/4Abstract.pdf

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

BU CLA MA 531 : Computability and Logic Handout 5 Assaf

Proof: Using induction, we define an infinite sequence of nodes x0, x1, . . ., forming an infinite path in T . At stage 0 of the induction, let x0 be the root of T , which has infinitely many successors by the hypothesis that T is infinite. At stage n ≥ 1, assume we have already selected nodes x0, x1, . . . , xn−1 so far, forming a path of length n−1, such that xn−1 has infinitely many successo...