Marco A. S. Souto

Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian

In this work, we study the existence of solutions for a class of problems involving p(x)-Laplacian operator in IR N. Using variational techniques we show some results of existence for a class of problems involving critical and subcritical growth.

Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains

We prove the existence of least energy nodal solution for a class of Schrödinger–Poisson system in a bounded domain

Quasilinear Problems Involving Changing-Sign Nonlinearities without an Ambrosetti–Rabinowitz-Type Condition

{\Omega \subset {\mathbb{R}}^3}

Some non-local logistic population model with non-zero boundary condition

Ω⊂R3 with nonlinearity having a subcritical growth.

Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions

Using variational methods, we establish the existence and multiplicity of positive solutions for the following class of problems: where λ,β∈(0,∞), q ∈(1,2*−1), 2*=2 N /( N −2), N ≥3, V,Z :ℝ N →ℝ are continuous functions verifying some hypotheses.

Superlinear problems without Ambrosetti and Rabinowitz growth condition

In this paper quasilinear elliptic boundary value equations without Ambrosetti and Rabinowitz growth condition are considered. Existence of a nontrivial solution result is established. For this, we show the existence of a Cerami’s sequence by using a variant of the Mountain Pass Theorem due to Schechter. The novelty here is that we may consider nonlinearities which satisfy a local p−superlinear condition and may change sign as well.

Existence of solutions for a class of nonlinear Schrödinger equations with potential vanishing at infinity

We prove that the semilinear elliptic equation , in , , on has a positive solution when the nonlinearity belongs to a class which satisfies at infinity and behaves like near the origin, where if and if . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of .

Schrödinger–Poisson equations without Ambrosetti–Rabinowitz condition☆

In this paper, we study some type of equations which may model the behavior of species inhabiting in some habitat. For our purpose, using a priori bounded techniques, we obtain a positive solution to a family of non-local partial differential equations with non-homogeneous boundary conditions.