• 대한수학회지
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• 제56권5호
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.245-253
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• 2011

Some new results on the intersection property of all nonzero solutions of a class of planar systems of Li$\acute{e}$nard type with vertical isoclines are obtained. The results of this paper generalize some previous results on this field.