Existence of Sign-Changing Solutions for a Class of p(x)-Biharmonic Kirchhoff-Type Equations

This paper mainly studies the existence of sign-changing solutions for the following px-biharmonic Kirchhoff-type equations: −a+b∫RN1p(x)|Δu|p(x)dxΔp(x)2u+V(x)|u|p(x)−2u = Kxf(u),x∈RN, where Δp(x)2u=Δ|Δu|p(x)−2Δu is the p(x) biharmonic operator, a,b>0 are constants, N≥2, V(x),K(x) are positive continuous functions which vanish at infinity, and the nonlinearity f has subcritical growth. Using the Nehari manifold method, deformation lemma, and other techniques of analysis, it is demonstrated that there are precisely two nodal domains in the problem’s least energy sign-changing solution ub. In addition, the convergence property of ub as b→0 is also established.