We use bifurcation theory to show the existence of infinitely many solutions at the first eigenvalue for a class of Dirichlet problems in one dimension. It has been observed that complexity of the solution curve for the boundary value problem u + λf(u) = 0 for 0 < x < L, u(0) = u(L) = 0 (1) seems to mirror that of the nonlinearity f(u), see e.g. P. Korman, Y. Li and T. Ouyang [6]. Namely, if f(...

Abstract The paper deals with the equation $$-\Delta u+a(x) u =|u|^{p-1}u $$ - Δ u + a ( x ) = | p 1 ...

We consider the following system of Schrödinger equations{−ΔU+λU=α0U3+βUV2−ΔV+μ(y)V=α1V3+βU2VinRN,N=2,3, where λ, α0, α1>0 are positive constants, β∈R is coupling constant, and μ:RN→R a potential function. Continuing work Lin Peng [6], we present solution type one species has peak at origin other many peaks over circle, but as seen in above, terms nonlinear.

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.

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.