Positive solutions of an indefinite prescribed mean curvature problem on a general domain
(2004) Advanced Nonlinear Studies — Vol. 4, n° 1, p. 1-13 (2004)
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- The existence of positive solutions is proved for the prescribed mean curvature problem -div (delu/root1+parallel todeluparallel to(2)) = lambdaf(x, u) + g(x, u) in Omega, u(x) = 0 on partial derivativeOmega, where Omega subset of R-N is a bounded smooth domain, not necessarily radially symmetric. We assume that integral(0)(u) f (x, s) ds is locally subquadratic at 0, integral(0)(u) g(x, s)ds is superquadratic at 0 and lambda > 0 is sufficiently small. A multiplicity result is also obtained, when integral(0)(u) f(x, s) ds has an oscillatory behaviour near 0. We allow f and g to change sign in any neighbourhood of 0.
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Habets, P., & Omari, P. (2004). Positive solutions of an indefinite prescribed mean curvature problem on a general domain. Advanced Nonlinear Studies, 4(1), 1-13. https://hdl.handle.net/2078.5/43647 (Original work published 2004)