A degree theory for a class of perturbed Fredholm maps.
A degree theory for a class of perturbed Fredholm maps. II.
A degree theory for compact perturbations of proper Fredholm mappings of index 0.
A degree theory for locally compact perturbations of Fredholm maps in Banach spaces.
A Hartman-Nagumo inequality for the vector ordinary -Laplacian and applications to nonlinear boundary value problems.
A new topological degree theory for densely defined quasibounded -perturbations of multivalued maximal monotone operators in reflexive Banach spaces.
A set of axioms for the degree of a tangent vector field on differentiable manifolds.
A topological version of the Ambrosetti-Prodi theorem
The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.
A transmission problem
A two parameters Ambrosetti-Prodi problem.
An Ambrosetti-Prodi-type problem for an elliptic system of equations via monotone iteration method and Leray-Schauder degree theory.
An application of the Leray-Schauder degree theory to boundary value problem for third and fourth order differential equations depending on the parameter
An elliptic equation with no monotonicity condition on the nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...
An extension of the topological degree in Hilbert space.
An index formula for the degree of (S)-mappings associated with one-dimensional -Laplacian.
An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations.
Approximation structures and applications to evolution equations.
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Bound sets and two-point boundary value problems for second order differential systems
The solvability of second order differential systems with the classical separated or periodic boundary conditions is considered. The proofs use special classes of curvature bound sets or bound sets together with the simplest version of the Leray-Schauder continuation theorem. The special cases where the bound set is a ball, a parallelotope or a bounded convex set are considered.
Boundary value problems for differential equations with deviating arguments