The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems
Pavel Drábek (1995)
Mathematica Bohemica
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We prove the existence of the least positive eigenvalue with a corresponding nonnegative eigenfunction of the quasilinear eigenvalue problem where is a bounded domain, is a real number and , satisfy appropriate growth conditions. Moreover, the coefficient contains a degeneration or a singularity. We work in a suitable weighted Sobolev space and prove the boundedness of the eigenfunction in . The main tool is the investigation of the associated homogeneous eigenvalue problem...