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Ding, Ling; Li, Lin; Zhang, Jin-Ling

Positive solutions for a nonhomogeneous Kirchhoff equation with the asymptotical nonlinearity in \(R^3\). (English) Zbl 1474.35298

Abstr. Appl. Anal. 2014, Article ID 710949, 10 p. (2014).
Summary: We study the following nonhomogeneous Kirchhoff equation: \(-(a + b \int_{R^3} | \nabla u |^2 d x) \Delta u + u = k(x) f(u) + h(x)\), \(x \in R^3\), \(u \in H^1(R^3)\), \(u > 0\), \(x \in R^3\), where \(f\) is asymptotically linear with respect to \(t\) at infinity. Under appropriate assumptions on \(k, f\), and \(h\), existence of two positive solutions is proved by using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.

Cited in 2 Documents

MSC:

35J60 Nonlinear elliptic equations
35B09 Positive solutions to PDEs
35J20 Variational methods for second-order elliptic equations
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References:

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