Ljusternik–Schnirelmann theory on $C^1$-manifolds

Abstract

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On the Spectrum of problems involving both p(x)-Laplacian and P(x)-Biharmonic

“…To attain this objective we will use a variational technique based on Ljusternick-Schnirelmann theory on C 1 -manifolds [11]. In fact, we give a direct characterization of λ k involving a mini-max argument over sets of genus greater than k.…”

Existence of solutions for a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions

“…To solve the eigenvalue problem (3.2), we will use the Ljusternik-schnirelmann theory on C 1 -manifolds (see [18] corollary 4.1). For any t > 0, denote by…”

“…[18] Suppose that M is a closed symmetric C 1 -manifold of a real Banach space E and 0 / ∈ M . Suppose also that f ∈ C 1 (M, IR) is even and bounded bellow.…”

The beginning of the Fucik spectrum for a Steklov problem

“…Proposition 2.1 is proved in [5] by applying a general result from infinite dimensional Ljusternik-Schnirelman theory (see [6]). In [5], the authors proved the simplicity, isolation and monotonicity with respect to the weight of the first eigenvalue λ 1 (m) of the Steklov eigenvalue problem 6.…”