1,720,996 research outputs found
Multiplicity and concentration results for a (p, q)-Laplacian problem in RN
Full text linkIn this paper, we study the multiplicity and concentration of positive solutions for the following (p, q)-Laplacian problem: {-Δpu-Δqu+V(εx)(|u|p-2u+|u|q-2u)=f(u)inRN,u∈W1,p(RN)∩W1,q(RN),u>0inRN,where ε> 0 is a small parameter, 1 < p< q< N, Δru=div(|∇u|r-2∇u), with r∈ { p, q} , is the r-Laplacian operator, V: RN→ R is a continuous function satisfying the global Rabinowitz condition, and f: R→ R is a continuous function with subcritical growth. Using suitable variational arguments and Ljusternik–Schnirelmann category theory, we investigate the relation between the number of positive solutions and the topology of the set where V attains its minimum for small ε
On a class of Kirchhoff problems via local mountain pass
No full textIn the present work we study the multiplicity and concentration of positive solutions for the following class of Kirchhoff problems: -{ε2 a + εb R3 δu 2 dx ) Δu + V (x)u= f(u) + γu5 in R3 , u ε H1 (R3) , u > 0 in R3 , where ε > 0 is a small parameter, a , b > 0 are constants, γ ε { 0 , 1 }, V is a continuous positive potential with a local minimum, and f is a superlinear continuous function with subcritical growth. The main results are obtained through suitable variational and topological arguments. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. Our theorems extend and improve in several directions the studies made in (Adv. Nonlinear Stud. 14 (2014), 483-510; J. Differ. Equ. 252 (2012), 1813-1834; J. Differ. Equ. 253 (2012), 2314-2351)
Topics in uniform continuity
No full textTe paper collects results and open problems concerning several classes of functions that generalize uniform continuity in various ways, including those metric spaces (generalizing Atsuji spaces) where all continuous functions have the property of being close to uniformly continuous
Multiple solutions for elliptic equations involving a general operator in divergence form
No full textIn this paper, exploiting variational methods, the existence of three weak solutions for a class of elliptic equations involving a general operator in divergence form and with Dirichlet boundary condition is investigated. Several special cases are analyzed. In conclusion, for completeness, a concrete example of an application is presented by finding the existence of three nontrivial weak solutions for an uniformly elliptic second-order problem on a bounded Euclidean domain
Yamabe-Type Equations on Carnot Groups
No full textThis article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain D of the Heisenberg group. Our approach is based on pure variational methods and locally sequentially weakly lower semicontinuous arguments
On doubly nonlocal fractional elliptic equations
No full textThis work is devoted to the study of the existence of solutions to nonlocal equations involving the fractional Laplacian. These equations have a variational structure and we find a nontrivial solution for them using the Mountain Pass Theorem. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. In addition, we require rather general assumptions on the local operator. As far as we know, this result is new and represent a fractional version of a classical theorem obtained working with Laplacian equations
On biharmonic equations with Navier boundary conditions
No full textIn this article, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the p-biharmonic operator is investigated. Moreover, a concrete example of an application is presented
Nonlinear Algebraic Systems with discontinuous terms
No full textUsing a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and positive definite matrix. Applications to tridiagonal, fourth-order and partial difference inclusions are presented
Existence and localization of solutions for nonlocal fractional equations
No full textThis work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the fractional Laplacian, finding a nontrivial weak solution of that equation
Nonlinear Neumann problems driven by a nonhomogeneous differential operator
No full textWe study a nonlinear parametric Neumann problem driven by a nonhomogeneous quasilinear elliptic differential operator div(a(x, del u)), a special case of which is the p-Laplacian. The reaction term is a nonlinearity function f which exhibits (p-1)-subcritical growth. By using variational methods, we prove a multiplicity result on the existence of weak solutions for such problems. An explicit example of an application is also presented
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