Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems

We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter λ > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution

Cyclic (Noncyclic) ϕ-condensing operator and its application to a system of differential equations

We establish a best proximity pair theorem for noncyclic ϕ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic ϕ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations

Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis

We give sufficient conditions for the existence of weak solutions to quasilinear elliptic Dirichlet problem driven by the A-Laplace operator in a bounded domain \u3c9. The techniques, based on a variant of the symmetric mountain pass theorem, exploit variational methods. We also provide information about the asymptotic behavior of the solutions as a suitable parameter goes to 0 + . In this case, we point out the existence of a blow-up phenomenon. The analysis developed in this paper extends and complements various qualitative and asymptotic properties for some cases described by homogeneous differential operators

The Existence of Solutions for Local Dirichlet (r(u), s(u))-Problems

In this paper, we consider local Dirichlet problems driven by the (r(u), s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r, s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument

Singular Anisotropic Problems with Competition Phenomena

We consider a Dirichlet problem driven by the anisotropic (p(z), q(z))-Laplacian, with a parametric reaction exhibiting the combined effects of singular and concave-convex nonlinearities. The superlinear term may change sign. Using variational tools together with truncation and comparison techniques, we prove a global (for the parameter ? > 0) existence and multiplicity theorem (a bifurcation-type theorem)

Solutions for parametric double phase Robin problems

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p - 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 +

Multiple solutions for semilinear Robin problems with superlinear reaction and no symmetries

We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered

Investigating Automatic Static Analysis Results to Identify Quality Problems: an Inductive Study

Background: Automatic static analysis (ASA) tools examine source code to discover "issues", i.e. code patterns that are symptoms of bad programming practices and that can lead to defective behavior. Studies in the literature have shown that these tools find defects earlier than other verification activities, but they produce a substantial number of false positive warnings. For this reason, an alternative approach is to use the set of ASA issues to identify defect prone files and components rather than focusing on the individual issues. Aim: We conducted an exploratory study to investigate whether ASA issues can be used as early indicators of faulty files and components and, for the first time, whether they point to a decay of specific software quality attributes, such as maintainability or functionality. Our aim is to understand the critical parameters and feasibility of such an approach to feed into future research on more specific quality and defect prediction models. Method: We analyzed an industrial C# web application using the Resharper ASA tool and explored if significant correlations exist in such a data set. Results: We found promising results when predicting defect-prone files. A set of specific Resharper categories are better indicators of faulty files than common software metrics or the collection of issues of all issue categories, and these categories correlate to different software quality attributes. Conclusions: Our advice for future research is to perform analysis on file rather component level and to evaluate the generalizability of categories. We also recommend using larger datasets as we learned that data sparseness can lead to challenges in the proposed analysis proces

Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA

The aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled \u201cCoincidence theorems for some multivalued mappings\u201d by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it

A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain

A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of R^N, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions