Existence of One-sign Solutions to the High-Dimensional Sign-Changing Weight p-Laplacian on General Domain
In this paper,we shall study the existence of one-sign solutions for thep-Laplacian problem:-div(φp(∇u))=γm(x)f(u),u(x)=0,x∈∂Ω,where Ω is a bounded domain in RN with a smooth boundary ∂Ω,and m(x)∈C((Ω))is a sign changing function,γ is a parameter,f∈C(R,R),sf(s)＞0 for s≠0.Based on the bifurcation result of Dai et al.[9,Theorem 5.1],we give the intervals for the parameter γ≠0 which ensure the existence of one-sign solutions for the above high-dimensional p-Laplacian problems if f0 ∉(0,∞)or f∞ ∉(0,∞),where f0=lim|s|→0 f(s)/φp(s),f∞=lim|s|→∞ f(s)/φp(s).We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.
unilateral global bifurcationhigh-dimensional sign-changing weight p-Laplacian problems on general domainone-sign solutions
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