Existence of a solution to a nonlinear equation |
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Authors: | AG Ramm |
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Institution: | Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA |
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Abstract: | Equation (−Δ+k2)u+f(u)=0 in D, u|∂D=0, where k=const>0 and D⊂R3 is a bounded domain, has a solution if is a continuous function in the region |u|?a, piecewise-continuous in the region |u|?a, with finitely many discontinuity points uj such that f(uj±0) exist, and uf(y)?0 for |u|?a, where a?0 is an arbitrary fixed number. |
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Keywords: | Nonlinear elliptic equations |
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