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Brezis [3]: find a function $u(x)$ and a constant $b$, satisfying \\[ \\Delta u+g(x,u)=p(x) \\;\\; \\mbox{in $D$} \\] \\[\n  u \\,| \\, _{\\partial D}=b, \\;\\;\\;\\; \\int_{\\partial D} \\frac{\\partial u}{\\partial n} \\, ds=0 \\,. \\] Here $D \\subset R^n$, is a bounded domain, with a smooth boundary. This problem can be seen as a PDE generalization of the periodic problem for one-dimensional pendulum-like equations. 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Temam [18], and H. Berestycki and H. Brezis [3]: find a function $u(x)$ and a constant $b$, satisfying \\[ \\Delta u+g(x,u)=p(x) \\;\\; \\mbox{in $D$} \\] \\[\n  u \\,| \\, _{\\partial D}=b, \\;\\;\\;\\; \\int_{\\partial D} \\frac{\\partial u}{\\partial n} \\, ds=0 \\,. \\] Here $D \\subset R^n$, is a bounded domain, with a smooth boundary. This problem can be seen as a PDE generalization of the periodic problem for one-dimensional pendulum-like equations. 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