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Multi-bump solutions for a Kirchhoff-type problem
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DOI：10.1515/anona-2015-0101.png)
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Abstract
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In this paper, we study the existence of solutions for the Kirchhoff problem {M(integral(R3)vertical bar del u vertical bar(2) dx + integral(R3) (lambda a(x) + 1)u(2) dx)(-Delta u + (lambda a(x) + 1)u) = f(u) in R-3, u is an element of H-1(R-3). Assuming that the nonnegative function a(x) has a potential well with int(a(-1) ({0})) consisting of k disjoint components Omega(1), Omega(2), ... , Omega(k) and the nonlinearity f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by using variational methods.
Keywords:
Kirchhoff problem
multi-bump solution
variational methods
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