Infinitely many sign-changing solutions for a Schrö dinger equation

Abstract

We study a superlinear Schrödinger equation in the whole Euclidean space ℝ n . By using a suitable sign-changing critical point, we prove that the problem admits infinitely many sign-changing solutions, under weaker conditions.

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

“…For a more complex situation, we refer the reader to [14]. The related studies on the elliptic equations also can be found in [15][16][17][18][19][20][21][22][23][24][25][26].…”

Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations

“…Obviously, we can prove that Φ satisfies condition (C) in the similar way as Lemma 2.3, and Φ(−u) = Φ(u) by using (F 5 ). Then, we only need to check conditions (A 1 ) and (A 2 ) of the fountain theorem (see [4,6,7,14,15,25]). …”

“…Finally, by the generalized mountain pass theorem (see [11,14,17,18,27]), for a given k ∈ N, there exists a critical point…”

Fixed Point Theory and Positive Solutions for a Ratio-Dependent Elliptic System

“…There is growing results about elliptic system, which comes from biological and physiological evidence, such as [1][2][3][4][5][6][7][8][9]. A more suitable general predator-prey model should be based on the so-called ratio-dependent theory, which asserts that the per capita predator growth rate should be a function of the ratio of prey to predator abundance.…”