In this paper we present a novel variational approach to the question of existence and multiplicity of positive solutions to semipositone problems in a bounded smooth domain of RN . We consider both the sublinear and superlinear cases.

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let π be a unitary, cuspidal, automorphic representation of GLn(AK). Let S be a set of finite places of K, such that the sum ∑ v∈S Nv −2/(n+1) is convergent. Then π is uniquely determined by the collection of the local components {πv | v 6∈ S, v finite} of π. Combining this theorem with base change, it is p...

In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with the multispecies structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system generically remains in a multispecies state. Even though for some of these species the replicative probability is very high, they are unable to invade the s...

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

1. Preliminaries 1 2. Multiplicity free actions 8 3. Linear multiplicity free actions 15 4. Examples of multiplicity free decompositions 21 5. A recursive criterion for multiplicity free actions 33 6. The classification of linear multiplicity free actions 37 7. Invariant polynomials and differential operators 43 8. Generalized binomial coefficients 52 9. Eigenvalues for operators in PD(V ) 61 R...