A symmetric solution of a multipoint boundary value problem with one-dimensional p-Laplacian at resonance Original Research Article

We apply an extension of Mawhin’s continuation theorem due to Ge to show the existence of at least one symmetric solution of the multipoint boundary value problem for the one-dimensional pp-Laplacian at resonance View the MathML source(ϕp(x′(t)))′=f(t,x(t),x′(t)),t∈(0,1), Turn MathJax on subject to the boundary conditions View the MathML sourcex(0)=∑i=1nμix(ξi),x(1)=∑i=1nμix(ηi), Turn MathJax on where View the MathML sourceϕp(s)=|s|p−2s,p>1,0<ξ1<ξ2<⋯<ξn<1/2,ξi+ηi=1,i=1,2,…,n,∑i=1nμi=1,f:[0,1]×R2→R with f(t,u,v)=f(1−t,u,−v)f(t,u,v)=f(1−t,u,−v) for (t,u,v)∈[0,1]×R2(t,u,v)∈[0,1]×R2, satisfying the Carathéodory conditions.