MULTIPLE SOLUTIONS RESULT FOR THE MIXED TYPE NONLINEAR ELLIPTIC PROBLEM

Multiple solutions for a fourth-order nonlinear elliptic problem

The existence of multiple solutions for a class of fourth-order elliptic equation with respect to the generalized asymptotically linear conditions is established by using the minimax method and Morse theory.

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Positive solutions for a nonlinear nonlocal elliptic transmission problem

K e y w o r d s E l l i p t i c system, Transmission problem, Positive solution. 1. I N T R O D U C T I O N Let 12 be a smooth bounded domain of R n, n > 2, and let ~1 c gl be a subdomain with smooth boundary ~ satisfying ~1 C i2. Writing F = c9~ and gl2 = ~\~l l we have ~ = ~1 tJ 122 and 0i'~2 = ~, tJ F. We are concerned with the existence of positive solutions to the following system of nonli...

Multiple Solutions for Nonlinear Elliptic Equations on Compact Riemannian Manifolds

Let (M, g) be a smooth, compact Riemannian n-manifold, and h be a Hölder continuous function on M . We prove the existence of multiple changing sign solutions for equations like ∆gu + hu = |u| ∗−2 u, where ∆g is the Laplace–Beltrami operator and the exponent 2∗ = 2n/ (n− 2) is critical from the Sobolev viewpoint.

Multiple Positive Solutions for Some Nonlinear Elliptic Systems

where k1, k2 > 0 are positive constants, Ω ⊂ R is a bounded domain with a smooth boundary ∂Ω and V (u, v) ∈ C(R,R). We refer to [CdFM], [CM], [dFF], [dFM] and [HvV] for variational study of such elliptic systems. However, it seems that the multiplicity of positive solutions for such elliptic systems is not well studied. Here, we study a case related to some models (with diffusion) in mathematic...