Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Orlicz Spaces and Nonlinear Elliptic Eigenvalue Problems

Nonlinear elliptic differential equations of order m acting in a space of m dimensions often occupy a special position in more general theories. In this paper we shall study one aspect of this situation. The nonlinear problem under consideration will be the variational approach to eigenvalue problems for nonlinear elliptic partial differential equations as developed by the author in [l], [2], [...

Multiple Solutions for Quasilinear Elliptic Neumann Problems in Orlicz-sobolev Spaces

Here, Ω is a bounded domain with sufficiently smooth (e.g. Lipschitz) boundary ∂Ω and ∂/∂ν denotes the (outward) normal derivative on ∂Ω. We assume that the function φ :R→R, defined by φ(s)= α(|s|)s if s = 0 and 0 otherwise, is an increasing homeomorphism from R to R. Let Φ(s)= ∫ s 0 φ(t)dt, s∈R. Then Φ is a Young function. We denote by LΦ the Orlicz space associated withΦ and by ‖ · ‖Φ the usu...

Multiple Solutions for Strongly Resonant Nonlinear Elliptic Problems with Discontinuities

We examine a nonlinear strongly resonant elliptic problem driven by the p-Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the liter...

An Orlicz-sobolev Space Setting for Quasilinear Elliptic Problems

In this paper we give two existence theorems for a class of elliptic problems in an Orlicz-Sobolev space setting concerning both the sublinear and the superlinear case with Neumann boundary conditions. We use the classical critical point theory with the Cerami (PS)-condition.

Multiple Solutions for Nonlinear Discontinuous Strongly Resonant Elliptic Problems

We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach uses the nonsmooth critical point theory for locally Lipschitz functionals due to Chang (1981) and ...