Journal
ACTA MATHEMATICA HUNGARICA
Volume 157, Issue 1, Pages 27-38Publisher
SPRINGER
DOI: 10.1007/s10474-018-0891-y
Keywords
logarithmic nonlinearity; ground state solution; sign-changing solution
Categories
Funding
- National Natural Science Foundation of China [11571370, 11701487, 11626202]
- Hunan Provincial Natural Science Foundation of China [2016JJ6137]
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We study elliptic equations with logarithmic nonlinearity. With the help of the constraint variational method, quantitative deformation lemma and some new energy inequalities, we establish the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. Our result complements the existing ones on Schrodinger problems since the logarithmic nonlinearity is sign-changing, and satisfies neither the monotonicity condition nor Ambrosetti-Rabinowitz condition.
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