Multiplicity of solutions for quasilinear elliptic equations

Bifurcation for Quasilinear Elliptic Singular BVP

“…See the works by Arcoya and Boccardo [4], Canino [15] and the references therein for the case of variational differential operators. See also the works by Andreu, Boccardo, Orsina and Segura de León [2], Andreu, Segura de León and Toledo [3] and Boccardo, Orsina and Porzio [14] for related parabolic problems.…”

Weak solutions of quasilinear elliptic PDE's at resonance

“…LEMMA 1. Let I be as in (9), with L as in (10) (10), let I be defined as in (9) (6) are in order: in [3] the assumption about g is that of superlinear growth at infinity and this leads to the usual estimates of superquadratic functionals; in [12] it is assumed that g is bounded while in our case (6) To conclude the proof of (i) we use the same device as in [7]. …”

“…We assume the ellipticity condition and the "usual" semipositivity condition (see [3]) on the matrix [s~aij (x, [8] and [9] is briefly outlined. Such theory has already been used by Canino to find weak solutions of quasilinear elliptic equations; in her paper she studied equation (1) with g(x, u) having a superlinear behaviour at infinity: under this assumption the functional satisfies the geometric requirements of the mountain pass theorem.…”

Quantitative deformation theorems and critical point theory

“…The results of this paper are developed in view of applications to nonsmooth variational problems, such as quasilinear elliptic problems of the type studied in [3,4] (see also the references in [4]). …”