1,721,080 research outputs found
On Problems Driven by the (p(·) , q(·)) -Laplace Operator
Full text linkThe aim of this paper is to prove the existence of at least one nontrivial weak solution for equations involving the (p(· ) , q(· ) ) -Laplace operator. The approach is variational and based on the critical point theory
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No full textNonhomogeneous Eigenvalue Problems with Singular and Critical Terms
No full textWe consider a parametric Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which has singular and critical terms. Using cut-off techniques and variational methods, we show that for all small values of the parameter λ > 0, the problem has a positive solution and this solution converges to 0 in C_0^1(\overline{\Omega}) as λ to 0^+
Parametric nonlinear nonhomogeneous Robin problems
No full textWe consider a Robin problem driven by a nonlinear nonhomogeneous differential operator plus a parametric potential term. The reaction is superlinear. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter lambda in R moves. Also we show the existence of a minimal positive solution and prove its monotonicity and continuity properties as a function of the parameter. Finally we show the existence of a nodal solution
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
POSITIVE SOLUTIONS FOR SINGULAR (p, q)-LAPLACIAN EQUATIONS WITH NEGATIVE PERTURBATION
Full text linkWe consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction consisting of a singular term plus a negative perturbation. Using regularization of the singular term and truncation and comparison techniques, we show that the problem has a unique positive smooth solution
Singular Neumann (p, q)-equations
Full text linkWe consider a nonlinear parametric Neumann problem driven by the sum of a p-Laplacian and of a q-Laplacian and exhibiting in the reaction the competing effects of a singular term and of a resonant term. Using variational methods together with suitable truncation and comparison techniques, we show that for small values of the parameter the problem has at least two positive smooth solutions
Nonlinear vector duffing inclusions with no growth restriction on the orientor field
Full text linkWe consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are -dense in the solution set of the convex problem (strong relaxation theorem
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