1,721,078 research outputs found
Nonlinear resonant periodic problems
No full textWe consider nonlinear periodic problems driven by the sum of a scalar p-Laplacian and a scalar Laplacian and a Caratheodory reaction, which at ±∞, is resonant with respect to any higher eigenvalue. Using variational methods, coupled with suitable perturbation and truncation techniques and Morse theory, we prove a three solutions theorem. For equations resonant with respect to the principal eigenvalue λ^0=0, we establish the existence of nodal solutions
Existence and multiplicity results for nonlinear eigenvalues problems with discontinuities
No full textOn p-logistic equations of equidiffusive type
No full textWe consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter varies. In the case of a unique positive solution , we investigate the monotonicity and continuity properties of the map
Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries
No full textWe consider a semilinear Dirichlet problem with an unbounded and indefinite potential and a superlinear reaction which need not satisfy the usual in such cases Ambrosetti-Rabinowitz condition. Using a combination of variational methods (critical point theory) with truncation and comparison techniques, with Morse theory and with flow invariance arguments, we show that the problems has at least seven nontrivial smooth solutions and provide sign information for all of them
Existence of two solutions for quasilinear periodic differential equations with discontinuities
Full text linksummary:In this paper we examine a quasilinear periodic problem driven by the one- dimensional -Laplacian and with discontinuous forcing term . By filling in the gaps at the discontinuity points of we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions, one positive, the other negative
Singular double phase problems with convection
Full text linkWe consider a nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a q-Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution
A class of nonlinear boundary value problems for second order vector differential equations
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