An elliptic resonance problem with multiple solutions

Multiple Solutions for an Elliptic Problem Related to Vortex Pairs

Multiple Solutions For Semilinear Elliptic Boundary Value Problems At Resonance

In recent years several nonlinear techniques have been very successful in proving the existence of weak solutions for semilinear elliptic boundary value problems at resonance. One technique involves a variational approach where solutions are characterized as saddle points for a related functional. This argument requires that the Palais-Smale condition and some coercivity conditions are satisfie...

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 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.

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...