Geodesic
Strong resonance problems for the one-dimensional $p$-Laplacian
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the existence of the weak solution of the nonlinear boundary-value problem $$\displaylines{ -(|u'|^{p-2}u')'= \lambda |u|^{p-2}u + g(u)-h(x)\quad \hbox{in } (0,\pi) ,\cr u(0)=u(\pi )=0\,, }$$ where $p$ and $\lambda$ are real numbers, $p, h\in L^{p'}(0,\pi ) (p' =\frac{p}{p-1})$ and the nonlinearity $g:\mathbb{R} \to \mathbb{R}$ is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of this problem.
Classification : 34B15, 34L30, 47J30
Keywords: p-Laplacian, resonance at the eigenvalues, landesman-lazer type conditions 
@article{EJDE_2005__2005__a295,
     author = {Bouchala, Jiri},
     title = {Strong resonance problems for the one-dimensional $p${-Laplacian}},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a295/}
}
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Bouchala, Jiri. Strong resonance problems for the one-dimensional $p$-Laplacian. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a295/