On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance

Georg Hetzer

Remarks on some nonlinear boundary value problems

Svatopluk Fučík (1976)

Commentationes Mathematicae Universitatis Carolinae

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Study of some noncooperative linear elliptic systems

Ali Djellit, Saadia Tas (2004)

Applications of Mathematics

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Using an approximation method, we show the existence of solutions for some noncooperative elliptic systems defined on an unbounded domain.

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 $\begin{matrix} - div (a (x, u) | |^{p - 2} \nabla u) = & {λ b (x, u) | u |}^{p - 2} u in Ω, u = & 0 on \partial Ω, \end{matrix}$ where $Ω$ is a bounded domain, $p > 1$ is a real number and $a (x, u)$ , $b (x, u)$ satisfy appropriate growth conditions. Moreover, the coefficient $a (x, u)$ contains a degeneration or a singularity. We work in a suitable weighted Sobolev space and prove the boundedness of the eigenfunction in $L^{\infty} (Ω)$ . The main tool is the investigation of the associated homogeneous eigenvalue problem...

Displaying similar documents to “On the existence of weak solutions for some quasilinear elliptic variational boundary value problems at resonance”

Remarks on some nonlinear boundary value problems

Study of some noncooperative linear elliptic systems

The least eigenvalues of nonhomogeneous degenerated quasilinear eigenvalue problems