In this paper, we prove that there exists at most one positive radial weak solution to the following quasilinear elliptic equation with singular critical growth

We prove some multiplicity results for a class of singular quasilinear elliptic problems involving the critical Hardy-Sobolev exponent and singularities on a half-space.

We prove that a variational quasilinear elliptic equation admits a positive weak solution on R n. Our results extend to a wider class of equations some known results about semilinear and quasilinear problems: all the coefficients involved (also the ones in the principal part) depend both on the variable x and on the unknown function u; moreover, they are not homogeneous with respect to u.

In this paper we study a quasilinear elliptic system coupled by Schrödinger equation with p-Laplacian operator and Poisson equation. Some scaling transformation ingenious methods are applied to produce the bounded Palais-Smale sequences existence of nontrivial solutions for is obtained mountain pass theorem.

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.