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This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.

Elliptic functions. --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Differential equations, Elliptic --- Mathematical analysis

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Complex analysis --- Algebraic geometry --- Number theory --- Elliptic functions --- 517.58 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials --- Nombres, Théorie des --- Modular functions. --- Fonctions modulaires --- Number theory. --- Nombres, Théories des --- Geometrie algebrique --- Fonctions elliptiques --- Formes automorphes --- Varietes abeliennes

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Number Theory --- Computational Complexity --- Elliptic functions --- Pi --- 517.58 --- 511.3 --- 510.5 --- Computational complexity --- Number theory --- 681.3*F2 --- Transcendental numbers --- Circle-squaring --- Number study --- Numbers, Theory of --- Algebra --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic --- Complexity, Computational --- Electronic data processing --- Machine theory --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Analytical, additive and other number-theory problems. Diophantine approximations --- Algorithms. Computable functions --- Analysis of algorithms and problem complexity--See also {681.3*B6}; {681.3*B7}; {681.3*F13} --- 681.3*F2 Analysis of algorithms and problem complexity--See also {681.3*B6}; {681.3*B7}; {681.3*F13} --- 510.5 Algorithms. Computable functions --- 511.3 Analytical, additive and other number-theory problems. Diophantine approximations --- 517.58 Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials. --- Special functions. Hyperbolic functions. Euler integrals. Gamma functions. Elliptic functions and integrals. Bessel functions. Other cylindrical functions. Spherical functions. Legendre polynomials. Orthogonal polynomials. Chebyshev polynomials