Geodesic
Singular Dirichlet boundary value problems. II: Resonance case
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 269-289

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Existence results are established for the resonant problem $y^{\prime \prime }+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_{{\mathrm loc}}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm{d}x \infty $.
Classification : 34B15, 34L30 
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     author = {O'Regan, Donal},
     title = {Singular {Dirichlet} boundary value problems. {II:} {Resonance} case},
     journal = {Czechoslovak Mathematical Journal},
     pages = {269--289},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {1998},
     mrnumber = {1624319},
     zbl = {0957.34016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1998__48_2_a5/}
}
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O'Regan, Donal. Singular Dirichlet boundary value problems. II: Resonance case. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 2, pp. 269-289. http://geodesic.mathdoc.fr/item/CMJ_1998__48_2_a5/