Indefinite Quasilinear Neumann Problem on Unbounded Domains

Neumann Problems with Indefinite and Unbounded Potential and Concave Terms

We consider a semilinear parametric Neumann problem driven by the negative Laplacian plus an indefinite and unbounded potential. The reaction is asymptotically linear and exhibits a negative concave term near the origin. Using variational methods together with truncation and perturbation techniques and critical groups, we show that for all small values of the parameter the problem has at least ...

The Neumann Problem on Lipschitz Domains

Au — 0 in D; u = ƒ on bD9 where ƒ and its gradient on 3D belong to L(do). For C domains, these estimates were obtained by A. P. Calderón et al. [1]. For dimension 2, see (d) below. In [4] and [5] we found an elementary integral formula (7) and used it to prove a theorem of Dahlberg (Theorem 1) on Lipschitz domains. Unknown to us, this formula had already been discovered long ago by Payne and We...

∂̄b-NEUMANN PROBLEM ON NONCHARACTERISTIC DOMAINS

We study the ∂̄b-Neumann problem for domains Ω contained in a strictly pseudoconvex manifold M2n+1 whose boundaries are noncharacteristic and have defining functions depending solely on the real and imaginary parts of a single CR function w. When the Kohn Laplacian is a priori known to have closed range in L2, we prove sharp regularity and estimates for solutions. We establish a condition on the...

Multiplicity of Solutions for a Class of Quasilinear Problem in Exterior Domains with Neumann Conditions

Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity

We consider a semilinear Neumann problem with an indefinite and unbounded potential and an asymmetric reaction that crosses at least the principal eigenvalue of the operator −Δ + βI in H1(Ω), β being the potential function. Using a combination of variational methods, with truncation and perturbation techniques and Morse theory, we prove multiplicity theorems providing precise sign information f...