Eigenvalue Problems and Bifurcation of Nonhomogeneous Semilinear Elliptic Equations in Exterior Strip Domains

We consider the following eigenvalue problems:[inline-graphic not available: see fulltext] in[inline-graphic not available: see fulltext] in[inline-graphic not available: see fulltext] where[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext] is a smooth bounded domain,[inline-graphic not available: see fulltext],[inline-graphic not available: see fulltext] is a smooth bounded domain in[inline-graphic not available: see fulltext] such that[inline-graphic not available: see fulltext]. Under some suitable conditions on[inline-graphic not available: see fulltext] and[inline-graphic not available: see fulltext], we show that there exists a positive constant[inline-graphic not available: see fulltext] such that the above-mentioned problems have at least two solutions if[inline-graphic not available: see fulltext], a unique positive solution if[inline-graphic not available: see fulltext], and no solution if[inline-graphic not available: see fulltext]. We also obtain some bifurcation results of the solutions at[inline-graphic not available: see fulltext].