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This paper investigates the existence and location of solutions for a Neumann problem driven by a (p , q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, which is its main novelty. This paper can be seen as the study of a quasilinear Neumann problem involving an elaborated perturbation with a Nemytskij operator. The approach proceeds through a version of the sub/supersolution method, exploiting an invariance property regarding the sub/supersolution ordered interval with respect to the intrinsic operator. An example illustrates the applicability of our result. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of anisotropic (→p, →q)-Laplacian problems with nonlinear right-hand sides that are superlinear at 1. We prove the existence of two nontrivial weak solutions to this kind of problem by applying an abstract critical point theorem under very general assumptions on the data without supposing the Ambrosetti-Rabinowitz condition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear right-hand side that does not satisfy the Ambrosetti-Rabinowitz condition. Based on an equivalent norm in the Musielak-Orlicz Sobolev space along with variational tools and critical point theory, we prove the existence of at least two nontrivial, bounded weak solutions. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem. [ABSTRACT FROM AUTHOR]

In this paper, a class of nonlinear differential boundary value problems with variable exponent is investigated. The existence of at least one non-zero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the quasilinear elliptic problem − Δ p u = a u + p − 1 − b u − p − 1 in Ω , u = constant on ∂ Ω , 0 = ∫ ∂ Ω | ∇ u | p − 2 ∇ u ⋅ ν d σ , where the operator is the p -Laplacian and the boundary condition is of type no-flux. In particular, we consider the Fučík spectrum of the p -Laplacian with no-flux boundary condition which is defined as the set Π p of all pairs (a , b) ∈ R 2 such that the problem above has a nontrivial solution. It turns out that this spectrum has a first nontrivial curve C being Lipschitz continuous, decreasing and with a certain asymptotic behavior. Since (λ 2 , λ 2) lies on this curve C , with λ 2 being the second eigenvalue of the corresponding no-flux eigenvalue problem for the p -Laplacian, we get a variational characterization of λ 2. This paper extends corresponding works for Dirichlet, Neumann, Steklov and Robin problems. [ABSTRACT FROM AUTHOR]