Geodesic
Positive Solutions to Weakly Nonlinear Elliptic Equations of Second Order on Cylindrical Domains
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
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     author = {V. A. Kondrat'ev},
     title = {Positive {Solutions} to {Weakly} {Nonlinear} {Elliptic} {Equations} of {Second} {Order} on {Cylindrical} {Domains}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {183--191},
     publisher = {mathdoc},
     volume = {250},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/TM_2005_250_a7/}
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V. A. Kondrat'ev. Positive Solutions to Weakly Nonlinear Elliptic Equations of Second Order on Cylindrical Domains. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 250 (2005), pp. 183-191. http://geodesic.mathdoc.fr/item/TM_2005_250_a7/