Singular quasilinear elliptic problems with convection terms

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray–Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis.

By means of lower and supper solutions method, we prove the existence and non-existence of ground state solutions for quasilinear elliptic equations with a convection term. Extending previous results of Goncalves and Silva (2010).

On the existence of multiple positive entire solutions for a quasilinear elliptic systems

Existence of unbounded positive solutions of quasilinear elliptic equations in two-dimensional exterior domains

In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly exploit sub-super-solution and truncation techniques, set-valued analysis, recursive methods, nonlinear regularity theory, as well as fixed point arguments. A uniqueness result is also presented.

The paper deals with the following problem:where is a parameter, and , . Under some certain assumptions on V(x), we establish the existence of ground-state solutions for quasi-linear elliptic equations with Sobolev exponent via the method of Pohožaev manifold, the monotonic trick and global compactness lemma. Some recent results are extended.

The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem.

Conditions for the existence of a fundamental solution of quasilinear elliptic equations and higher-order systems with discontinuous coefficients

On various questions of the existence of an approximate solution for quasilinear elliptic equations and systems in S. L. Sobolev spaces

We establish existence and regularity of positive solutions for a class of quasilinear elliptic systems with singular and superlinear terms. The approach is based on sub-supersolution methods for systems of quasilinear singular equations and the Schauder's fixed point Theorem.

This paper studies the existence of solutions for Robin problems involving p ( x )-Laplacian-like operators which arise from capillarity phenomena. When we only consider the convective term, due to the lack of a variational structure, the well-known variational methods are not applicable. Using Galerkin method together with Brouwer’s fixed point theorem, we obtain the existence of finite-dimensional approximate solution and generalized solution. On the other hand, utilizing local linking theorem without Ambrosetti-Rabinowitz ((A-R) for short) condition, we obtain the existence of a nontrivial solution under some conditions. The main difficulties and innovations of the present article are that we consider the convective term, the weaker assumptions on the nonlinear term, and p ( x )-Laplacian-like operators with Robin boundary condition.

Positive solutions of quasilinear elliptic equations with exponential nonlinearity combined with convection term

We prove the existence and regularity of solutions for a quasi-linear elliptic system with convection terms that can be singular in the solution and its gradient. Comparison properties and a priori estimates are also obtained. Our approach relies on invariance, regularity, strong maximum principle, and fixed-point arguments.

Existence and regularity of solutions of quasilinear elliptic equations in nonsmooth domains have been interesting topics in the development of partial differential equations. The existence of finite-energy solutions of higher-order equations, also those with degenerations and singularities, can be shown by theories of monotone operators and topological methods. There are few results about singular solutions of second-order equations involving the p-Laplacian with the Dirac distribution on the right-hand side. So far the existence of singular solutions of higher-order equations with a prescribed asymptotic behavior has not been investigated. The aims of my dissertation are to look for finite-energy and singular solutions of quasilinear elliptic equations on manifolds with conic points. We single out realizations of the p-Laplacian in particular, (p>= 2), and a cone-degenerate operator in general, which are shown to belong to the class (S)_+. Assuming further coercivity conditions and employing mapping degree theory for generalized monotone mappings, we obtain existence for the prototypical example of the p-Laplacian and for general higher-order equations.

An existence result for a class of quasilinear singular competitive elliptic systems