Leray–Lions type [formula omitted]-biharmonic equations involving Hardy potentials

Abstract

In this article, we investigate p(x)-biharmonic equations involving Leray–Lions type operators and Hardy potentials. Leray–Lions type operators include p-Laplacian, p-Laplacian-like, p(x)-Laplacian, (p,q)-Laplacian, (p(x),q(x))-Laplacian operators and so forth. Moreover, fourth-order Leray–Lions type elliptic equations with variable exponents are seldom mentioned in previous papers. Some new theorems of the existence on the generalized solutions are reestablished for such equations when the Leray–Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.