Nonlinear eigenvalue problems for quasilinear systems

Quasilinear Elliptic Systems of Resonant Type and Nonlinear Eigenvalue Problems

Nonlinear Transmission Problems for Quasilinear Parabolic Systems

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

A note on quasilinear elliptic eigenvalue problems

We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

Eigenvalue Problems for a Quasilinear Elliptic Equation on Rn

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...

Eigenvalue problems for a quasilinear elliptic equation on ℝN

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...