Existence of solution for a class of semilinear elliptic problems at double resonance

The Beginning of the Fučik Spectrum for the p-Laplacian

“…The result of Theorem 5.1 is of the same type as that of [12] where p=2 and :=;, of [14] where p=2 and N=1 and of [18] where p=2 (see Remark 5.2 below for a precise comparison). It improves the result of [3] where :=; and where the strict inequalities in (F) are imposed on # \ (x),…”

Multiple Periodic Solutions of Second-Order Ordinary Differential Equations Across Resonance

“…to control the interference of the nonlinearity with the eigenvalues of the associated linear problem (see [4,5,8,9,10,15,17,18,20,23,26]). Among these works, Fabry and Fonda [15], Omari and Zanolin [26] established the solvability of (1.1) under the following so-called double-resonance conditions for some k ∈ N and uniformly for a.e.…”

Existence of solution for a class of biharmonic equations

“…To the best of our knowledge, the solvability of boundary value problem (1.1) has not been studied till now. The main purpose of this paper is to extend some of the results known in [1], concerning the Dirichlet problem (1.3) to the biharmonic problem (1.1) with Navier boundary condition. Our main result is the following :…”

“…See for instance [6], [1] and the references given there. To the best of our knowledge, the solvability of boundary value problem (1.1) has not been studied till now.…”