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Zbl 0816.35031
El Hachimi, A.; Gossez, J.-P.
(Hachimi, A.el)
A note on a nonresonance condition for a quasilinear elliptic problem.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 22, No.2, 229-236 (1994). ISSN 0362-546X

The authors study sufficient conditions for nonresonance of the problem $$-\text {div}(\vert \nabla u\vert\sp{p-2} \nabla u)= f(u)+ h(x) \quad (x\in \Omega), \qquad u=\varphi \quad (x\in \partial \Omega),$$ i.e. existence of solutions for any given $h\in L\sb \infty (\Omega)$ and $\varphi\in W\sb p\sp{1-1/p} (\partial \Omega)\cap L\sb \infty (\partial \Omega)$. Typically, these conditions are formulated in terms of the interaction'' of the asymptotic growth of the primitive of the nonlinearity $f$, on the one hand, and the first eigenvalue of the above differential operator, on the other.
[J.Appell (Würzburg)]
MSC 2000:
*35J65 (Nonlinear) BVP for (non)linear elliptic equations
35A05 General existence and uniqueness theorems (PDE)
35P30 Nonlinear eigenvalue problems for PD operators

Keywords: nonresonance

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