Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schrödinger equations in bounded domains

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

Infinitely Many Solutions for Fractional Schrödinger-poisson Systems with Sign-changing Potential

In this article, we prove the existence of multiple solutions for following fractional Schrödinger-Poisson system with sign-changing potential (−∆)u+ V (x)u+ λφu = f(x, u), x ∈ R, (−∆)φ = u, x ∈ R, where (−∆)α denotes the fractional Laplacian of order α ∈ (0, 1), and the potential V is allowed to be sign-changing. Under certain assumptions on f , we obtain infinitely many solutions for this sys...

Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

and Applied Analysis 3 where a ∈ [0, π), b ∈ C([0, 1], [0, +∞)) and c, γ > 0. It is easy to verify that all conditions ofTheorem 4 are satisfied. So, BVP (1)with the nonlinear term (10) has at least two solutions, one positive and the other negative. Reference [7, Theorem 3.3] can only guarantee a nonzero solution for this example. Theorem 7. Assume that (H1)–(H5) hold. Then, BVP (1) has at lea...

existence of infinitely many solutions for coupled system of schrödinger-maxwell's equations