Sign-changing critical points via Sandwich Pair theorems

Sign-changing Critical Points from Linking Type Theorems

In this paper, the relationships between sign-changing critical point theorems and the linking type theorems of M. Schechter and the saddle point theorems of P. Rabinowitz are established. The abstract results are applied to the study of the existence of sign-changing solutions for the nonlinear Schrödinger equation −∆u+V (x)u = f(x, u), u ∈ H1(RN ), where f(x, u) is a Carathéodory function. Pr...

Transfer Theorems via Sign Conditions

L-Fuzzy Fixed Points Theorems for L-Fuzzy Mappings via βℱL-Admissible Pair

We define the concept of βℱL-admissible for a pair of L-fuzzy mappings and establish the existence of common L-fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result.

On Generalized “ham Sandwich” Theorems

In this short note we utilize the Borsuk-Ulam Anitpodal Theorem to present a simple proof of the following generalization of the “Ham Sandwich Theorem”: Let A1, . . . , Am ⊆ R be subsets with finite Lebesgue measure. Then, for any sequence f0, . . . , fm of R-linearly independent polynomials in the polynomial ring R[X1, . . . , Xn] there are real numbers λ0, . . . , λm, not all zero, such that ...

Auxiliary relations and sandwich theorems

Below let II = [0, 1]. A well-known topological theorem due to Katětov states: Suppose (X, τ) is a normal topological space, and let f : X → II be upper semicontinuous, g : X → II be lower semicontinuous, and f ≤ g. Then there is a continuous h : X → II such that f ≤ h ≤ g. Recall that f : X → II is upper semicontinuous if f is continuous from (X, τ) to (II, ω); lower semicontinuous if continuo...