1,720,990 research outputs found
Multiplicity theorems for discrete boundary value problems
No full textIn this paper we study a boundary value problem for difference equations in a variational framework. We establish the existence of at least three solutions for a perturbed problem using a recent result by Ricceri, in which the non-convexity of a superlevel of a suitable functional is assumed
Well posed optimization problems and nonconvex Chebyshev sets in Hilbert spaces
No full textA result on the existence and uniqueness of metric projection for certain sets is proved, by means of a saddle point theorem. A conjecture, based on such a result and aiming for the construction of a nonconvex Chebyshev set in a Hilbert space, is presented
A multiplicity theorem for a perturbed second order nonautonomous system
No full textIn this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least k connected components, then our problem has at least k periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
No full textA recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented
Three solutions for a Dirichlet problem with one-sided growth conditions on the nonlinearities
No full textWe consider a semilinear elliptic partial differential equation, depending on two positive parameters λ and μ, coupled with homogeneous Dirichlet boundary conditions. Assuming only one-sided growth conditions on the nonlinearities involved, we prove the existence of at least three weak solutions for λ and μ lying in convenient intervals. We employ techniques of nonsmooth analysis introduced by Degiovanni and Zani, and a theorem of Ricceri for multiplicity of local minimizers
Low-dimensional compact embeddings of symmetric Sobolev spaces with applications
No full textIf Omega is an unbounded domain in R^N and p > N, the Sobolev space W^(1,p)(Omega) is not compactly embedded into L^infinity(Omega). Nevertheless, we prove that if Omega is a strip-like domain, then the subspace of W^(1,p)(Omega) consisting of the cylindrically symmetric functions is compactly embedded into L^infinity(Omega). As an application, we study a Neumann problem involving the p-Laplacian operator and an oscillating nonlinearity, proving the existence of infinitely many weak solutions. Analogous results are obtained for the case of partial symmetry
Infinitely many bounded solutions for the p-Laplacian with nonlinear boundary conditions
No full textBy applying a method due to Saint Raymond, we prove the existence of infinitely many weak solutions for a quasilinear elliptic partial differential equation, involving the p-Laplacian operator, coupled with a nonlinear boundary condition. Our main assumption is a suitable oscillatory behaviour of the nonlinearity either at infinity or at zero
Three nonzero periodic solutions for a differential inclusion
No full textWe prove the existence of three non-zero periodic solutions for an ordinary differential inclusion. Our approach is variational and based on a multiplicity theorem for the critical points of a nonsmooth functional, which extends a recent result of Ricceri
On a problem of Huang concerning best constants in Sobolev embeddings
No full textAnswering a question raised by Y.X. Huang, we prove what follows: if O is a bounded smooth domain and p > 1, then the mapping q → λq |O|^(p/q) is decreasing in ]0, p*[ and Lipschitz continuous on compact subsets of ]0, p*[, λq being the p-th power of the best Sobolev constant for the embedding of W^(1,p)(O) into L^q(O
Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions
Full text linkThrough variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function u, and prove that the set of bifurcation points for the solutions of the system is not σ-compact. Then, we deal with a linear system depending on a real parameter λ > 0 and on a function u, and prove that there exists λ* such that the set of the functions u, such that the system admits nontrivial solutions, contains an accumulation point
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