Geodesic
Differential equations at resonance
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 673-694.

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New existence results are presented for the two point singular ``resonant'' boundary value problem $\frac{1}{p}(py')'+r y+\lambda_m qy=f(t,y,py')$ a.e\. on $[0,1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here $\lambda_m$ is the $(m+1)^{st}$ eigenvalue of $\frac{1}{pq} [(pu')' +rpu] +\lambda u=0$ a.e\. on $[0,1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data.
Classification : 34B15, 34B24
Keywords: boundary value problems; resonance; existence 
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     author = {O'Regan, Donal},
     title = {Differential equations at resonance},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {673--694},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {1995},
     mrnumber = {1378689},
     zbl = {0843.34029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995__36_4_a5/}
}
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O'Regan, Donal. Differential equations at resonance. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 4, pp. 673-694. http://geodesic.mathdoc.fr/item/CMUC_1995__36_4_a5/