Multi-layer solutions for an elliptic problem

Concentrating solutions for an anisotropic elliptic problem with large exponent

We consider the following anisotropic boundary value problem ∇(a(x)∇u) + a(x)u = 0, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ R2 is a bounded smooth domain, p is a large exponent and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of concentrating solutions. We show that at a given strict local maximum point of a(x), there exist arbitraril...

Multiple Solutions for an Elliptic Problem Related to Vortex Pairs

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

analytic solutions for the stephen's inverse problem with local boundary conditions including elliptic and hyperbolic equations

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

Multiple Clustered Layer Solutions for Semilinear Elliptic Problems on S

We consider the following superlinear elliptic equation on Sn  ε∆Snu− u+ f(u) = 0 in D; u > 0 in D and u = 0 on ∂D, where D is a geodesic ball on Sn with geodesic radius θ1, and ∆Sn is the Laplace-Beltrami operator on Sn. We prove that for any θ ∈ ( 2 , π) and for any positive integer N ≥ 1, there exist at least 2N + 1 solutions to the above problem for ε sufficiently small. Moreover, the asym...