1,721,033 research outputs found
Positive solutions for singular (p, 2)-equations
Full text linkWe consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a (p- 1) -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions
Landesman-Lazer type (p,q)-equations with Neumann condition
Full text linkWe consider a Neumann problem driven by the (p,q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of calculus of variations, we show that the problem has at least one nontrivial weak solution
Multiple Solutions with Sign Information for a Class of Coercive (p, 2)-Equations
Full text linkWe consider a nonlinear Dirichlet equation driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation). The hypotheses on the reaction f(z, x) are minimal and make the energy (Euler) functional of the problem coercive. We prove two multiplicity theorems producing three and four nontrivial smooth solutions, respectively, all with sign information. We apply our multiplicity results to the particular case of a class of parametric (p, 2)-equations
Superlinear Robin Problems with Indefinite Linear Part
Full text linkWe consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang
Parametric nonlinear singular Dirichlet problems
Full text linkWe consider a nonlinear parametric Dirichlet problem driven by the p-Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions
Nonlinear multivalued Duffing systems
No full textWe consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita–Kowalski [7]
Multiple solutions for (p,2)-equations at resonance
Full text linkWe consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian and a Laplacian and a reaction term which is (p− 1)-linear near ±∞ and resonant with respect to any nonprincipal variational eigenvalue of (−∆p, W01,p(Ω)). Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them
NONLINEAR ROBIN PROBLEMS WITH UNILATERAL CONSTRAINTS AND DEPENDENCE ON THE GRADIENT
Full text linkWe consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution
Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth
Full text linkWe consider a nonlinear elliptic problem driven by the Dirichlet -Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term . Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution
Multiple solutions for strongly resonant Robin problems
No full textWe consider nonlinear (driven by the p-Laplacian) and semilinear Robin problems with indefinite potential and strong resonance with respect to the principal eigenvalue. Using variational methods and critical groups, we prove four multiplicity theorems producing up to four nontrivial smooth solutions
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