Geodesic
Positive Solutions to Weakly Nonlinear Elliptic Equations of Second Order on Cylindrical Domains
Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 183-191

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Solutions to second-order semilinear elliptic equations in cylindrical domains are studied. Conditions for the existence and nonexistence of positive solutions satisfying the zero Dirichlet or Neumann boundary conditions on the lateral surface are obtained. 
@article{TRSPY_2005_250_a7,
     author = {V. A. Kondrat'ev},
     title = {Positive {Solutions} to {Weakly} {Nonlinear} {Elliptic} {Equations} of {Second} {Order} on {Cylindrical} {Domains}},
     journal = {Informatics and Automation},
     pages = {183--191},
     publisher = {mathdoc},
     volume = {250},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a7/}
}
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V. A. Kondrat'ev. Positive Solutions to Weakly Nonlinear Elliptic Equations of Second Order on Cylindrical Domains. Informatics and Automation, Differential equations and dynamical systems, Tome 250 (2005), pp. 183-191. http://geodesic.mathdoc.fr/item/TRSPY_2005_250_a7/