1,721,047 research outputs found
Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence
Full text linkThe paper focuses on a Dirichlet problem driven by the (p,q)-Laplacian containing a parameter in the principal part of the elliptic equation and a (convection) term fully depending on the solution and its gradient. Existence of solutions, uniqueness, a priori estimates, and asymptotic properties as and are established under suitable conditions
Constant sign and sign-changing solutions for quasilinear elliptic equations with Neumann boundary condition
No full textThrough variational methods, sub-supersolution and truncation techniques we prove the existence
of three nontrivial solutions for a quasilinear elliptic equation with Neumann boundary
condition. We provide sign information for each of these solutions: two of them are of opposite
constant sign and the third one is sign changing
A sub-supersolution approach for Neumann boundary value problems with gradient dependence
No full textExistence and location of solutions to a Neumann problem driven by an nonhomogeneous differential operator and with gradient dependence are established developing a non-variational approach based on an adequate method of sub-supersolution. The abstract theorem is applied to prove the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems
Critical points for a class of nondifferentiable functions and applications
No full textSome critical point theorems involving functional that are the sum of a locally Lipschitz continuous term and of a convex, proper, besides lower semicontinuous, function are established. A recent existence result of Adly, Buttazzo, and Théra [1, Theorem 2.3] is improved. Applications to elliptic variational-hemivariational inequalities are then examined
Positive, negative, and nodal solutions to elliptic differential inclusions depending on a parameter
No full textThe homogeneous Dirichlet problem for a partial differential inclusion involving the p-Laplace operator and depending on a parameter λ > 0 is investigated. The existence of three smooth solutions, a smallest positive, a biggest negative, and a nodal one, is obtained for any λ sufficiently large by combining variational methods with truncation techniques
A sub-supersolution approach for robin boundary value problems with full gradient dependence
Full text linkThe paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A subsupersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions
Multiple solutions for a class of elliptic hemivariational inequalities
No full textThe existence of multiple solutions to elliptic hemivariational inequality problems in bounded domains is investigated via a suitable nonsmooth version of a classical technique due to Struwe and a recent saddle point theorem for locally Lipschitz continuous functionals
Critical points for nondifferentiable functions in presence of splitting
No full textAbstractA classical critical point theorem in presence of splitting established by Brézis–Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational–hemivariational eigenvalue problems
Nonlinear difference equations through variational methods
No full textA careful arrangement of some recent results on the existence and multiplicity of solutions for nonlinear difference equations involving the discrete p-Laplacian is given. Main tools are critical points
theorems presented below
Bounded Palais-Smale sequences for non-differentiable functions
No full textThe existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved
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