Geodesic
Existence and multiplicity of positive solutions for a singular problem associated to the $p$-Laplacian operator
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: Consider the problem $$ -\Delta_{p}u=g(u) +\lambda h(u)\quad\hbox{in }\Omega $$ with $u=0$ on the boundary, where $\lambda\in(0,\infty), \Omega$ is a strictly convex bounded and $C^{2}$ domain in $\mathbb{R}^{N}$ with $N\geq2$, and $1 less than p\leq2. Under suitable assumptions on $g$ and $h$ that allow a singularity of $g$ at the origin, we show that for $lambda$ positive and small enough the above problem has at least two positive solutions in $C(overlineOmega)capC^1(Omega)$ and that $lambda=0$ is a bifurcation point from infinity. The existence of positive solutions for problems of the form $-Delta_pu=K(x) g(u)+lambdah(u)+f(x)$ in $Omega, u=0$ on $partialOmega$ is also studied.$
Classification : 35J60, 35J65
Keywords: singular problems, p-Laplacian operator, nonlinear eigenvalue problems 
@article{EJDE_2004__2004__a189,
     author = {Aranda, Carlos and Godoy, Tomas},
     title = {Existence and multiplicity of positive solutions for a singular problem associated to the $p${-Laplacian} operator},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a189/}
}
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Aranda, Carlos; Godoy, Tomas. Existence and multiplicity of positive solutions for a singular problem associated to the $p$-Laplacian operator. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a189/