Infinitely many non-radial singular solutions of

Infinitely many radial solutions for the fractional Schrödinger-Poisson systems

In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator { (−∆)su+ V (|x|)u+ φ(|x|, u) = f(|x|, u), x ∈ R3, (−∆)tφ = u2, x ∈ R3, (1) where (−∆)s(s ∈ (0, 1)) and (−∆)t(t ∈ (0, 1)) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions. c ©2016 All rights reserved.

Infinitely Many Solutions of Superlinear Elliptic Equation

and Applied Analysis 3 Lemma 6 (see [17]). Assume that |Ω| < ∞, 1 ≤ p, r ≤ ∞, f ∈ C(Ω×R), and |f(x, u)| ≤ c(1+|u|). Then for every

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.

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

Non-radial Singular Solutions of Lane-emden Equation in R

We obtain infinitely many non-radial singular solutions of LaneEmden equation ∆u + u = 0 in RN\{0}, N ≥ 4 with N + 1 N − 3 < p < pc(N − 1) by constructing infinitely many radially symmetric regular solutions of equation on SN−1 ∆SN−1w − 2 p− 1 [ N − 2− 2 p− 1 ] w + w = 0.